This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
| Index |
Inference Rule |
Input latex |
Feeds latex |
Output latex |
step validity |
dimension check |
unit check |
notes |
|
11
|
declare initial expr |
|
|
-
2103023049; locally 3077940:
\(\sin(x) = \frac{1}{2i}\left(\exp(i x)-\exp(-i x) \right)\)
\(\sin{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464} pdg_{4621}} - e^{- pdg_{1464} pdg_{4621}}}{2 pdg_{4621}}\)
|
no validation is available for declarations |
2103023049:
|
2103023049:
|
|
|
26
|
simplify |
-
1128605625; locally 6426652:
\({\rm sech}^2\ x + \tanh^2(x) = \frac{4}{\left(\exp(x)+\exp(-x)\right)^2} + \frac{\left(\exp(x)-\exp(-x)\right)^2}{\left(\exp(x)+\exp(-x)\right)^2}\)
\(\tanh^{2}{\left(pdg_{1464} \right)} + \operatorname{sech}^{2}{\left(pdg_{1464} \right)} = \frac{\left(e^{pdg_{1464}} - e^{- pdg_{1464}}\right)^{2}}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}} + \frac{4}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}}\)
|
|
-
4830221561; locally 6070484:
\({\rm sech}^2\ x + \tanh^2(x) = \frac{4+\left(\exp(2x)-1-1+\exp(-2x)\right)}{\left(\exp(x)+\exp(-x)\right)^2}\)
\(\tanh^{2}{\left(pdg_{1464} \right)} + \operatorname{sech}^{2}{\left(pdg_{1464} \right)} = \frac{e^{2 pdg_{1464}} + 2 + e^{- 2 pdg_{1464}}}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}}\)
|
valid |
1128605625:
4830221561:
|
1128605625:
4830221561:
|
|
|
25
|
add expr 1 to expr 2 |
-
3868998312; locally 5395954:
\({\rm sech}^2\ x = \frac{4}{\left(\exp(x)+\exp(-x)\right)^2}\)
\(\operatorname{sech}^{2}{\left(pdg_{1464} \right)} = \frac{4}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}}\)
-
2121790783; locally 9317216:
\(\tanh^2(x) = \frac{ \left(\exp(x)-\exp(-x)\right)^2}{\left(\exp(x)+\exp(-x)\right)^2}\)
\(\tanh^{2}{\left(pdg_{1464} \right)} = \frac{\left(e^{pdg_{1464}} - e^{- pdg_{1464}}\right)^{2}}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}}\)
|
|
-
1128605625; locally 6426652:
\({\rm sech}^2\ x + \tanh^2(x) = \frac{4}{\left(\exp(x)+\exp(-x)\right)^2} + \frac{\left(\exp(x)-\exp(-x)\right)^2}{\left(\exp(x)+\exp(-x)\right)^2}\)
\(\tanh^{2}{\left(pdg_{1464} \right)} + \operatorname{sech}^{2}{\left(pdg_{1464} \right)} = \frac{\left(e^{pdg_{1464}} - e^{- pdg_{1464}}\right)^{2}}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}} + \frac{4}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}}\)
|
valid |
3868998312:
2121790783:
1128605625:
|
3868998312:
2121790783:
1128605625:
|
|
|
15
|
declare initial expr |
|
|
-
4585932229; locally 4731536:
\(\cos(x) = \frac{1}{2}\left(\exp(i x)+\exp(-i x) \right)\)
\(\cos{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464} pdg_{4621}}}{2} + \frac{e^{- pdg_{1464} pdg_{4621}}}{2}\)
|
no validation is available for declarations |
4585932229:
|
4585932229:
|
|
|
19
|
substitute LHS of expr 1 into expr 2 |
-
6404535647; locally 4319733:
\(\cosh x = \frac{\exp(x) + \exp(-x)}{2}\)
\(\cosh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\)
-
7731226616; locally 3909583:
\({\rm sech}\ x = \frac{1}{\cosh x}\)
\(\operatorname{sech}{\left(pdg_{1464} \right)} = \frac{1}{\cosh{\left(pdg_{1464} \right)}}\)
|
|
-
4166155526; locally 7222556:
\({\rm sech}\ x = \frac{2}{\exp(x)+\exp(-x)}\)
\(\operatorname{sech}{\left(pdg_{1464} \right)} = \frac{2}{e^{pdg_{1464}} + e^{- pdg_{1464}}}\)
|
valid |
6404535647:
error for dim with 6404535647
7731226616:
4166155526:
|
6404535647:
N/A
7731226616:
4166155526:
|
|
|
21
|
substitute LHS of expr 1 into expr 2 |
-
1038566242; locally 3145608:
\(\sinh x = \frac{\exp(x) - \exp(-x)}{2}\)
\(\sinh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}\)
-
4872163189; locally 3867418:
\(\tanh(x) = \frac{\sinh(x)}{\cosh(x)}\)
\(\tanh{\left(pdg_{1464} \right)} = \frac{\sinh{\left(pdg_{1464} \right)}}{\cosh{\left(pdg_{1464} \right)}}\)
|
|
-
2902772962; locally 6831354:
\(\tanh(x) = \frac{\frac{1}{2}\left( \exp(x)-\exp(-x) \right)}{\cosh(x)}\)
\(\tanh{\left(pdg_{1464} \right)} = \frac{\frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}}{\cosh{\left(pdg_{1464} \right)}}\)
|
valid |
1038566242:
4872163189:
2902772962:
|
1038566242:
4872163189:
2902772962:
|
|
|
27
|
simplify |
-
4830221561; locally 6070484:
\({\rm sech}^2\ x + \tanh^2(x) = \frac{4+\left(\exp(2x)-1-1+\exp(-2x)\right)}{\left(\exp(x)+\exp(-x)\right)^2}\)
\(\tanh^{2}{\left(pdg_{1464} \right)} + \operatorname{sech}^{2}{\left(pdg_{1464} \right)} = \frac{e^{2 pdg_{1464}} + 2 + e^{- 2 pdg_{1464}}}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}}\)
|
|
-
5866629429; locally 8702257:
\({\rm sech}^2\ x + \tanh^2(x) = 1\)
\(\tanh^{2}{\left(pdg_{1464} \right)} + \operatorname{sech}^{2}{\left(pdg_{1464} \right)} = 1\)
|
valid |
4830221561:
5866629429:
|
4830221561:
5866629429:
|
|
|
2
|
declare initial expr |
|
|
-
1038566242; locally 3145608:
\(\sinh x = \frac{\exp(x) - \exp(-x)}{2}\)
\(\sinh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}\)
|
no validation is available for declarations |
1038566242:
|
1038566242:
|
|
|
12
|
change variable X to Y |
-
2103023049; locally 3077940:
\(\sin(x) = \frac{1}{2i}\left(\exp(i x)-\exp(-i x) \right)\)
\(\sin{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464} pdg_{4621}} - e^{- pdg_{1464} pdg_{4621}}}{2 pdg_{4621}}\)
|
-
6976493023:
\(x\)
\(pdg_{1464}\)
-
7159989263:
\(i x\)
\(pdg_{1464} pdg_{4621}\)
|
-
4878728014; locally 5823930:
\(\sin(i x) = \frac{1}{2i}\left(\exp(-x) - \exp(x) \right)\)
\(\sin{\left(pdg_{1464} pdg_{4621} \right)} = \frac{- e^{pdg_{1464}} + e^{- pdg_{1464}}}{2 pdg_{4621}}\)
|
LHS diff is 0
RHS diff is exp(pdg1464)/(2*pdg4621) + exp(pdg1464*pdg4621**2)/(2*pdg4621) - exp(-pdg1464*pdg4621**2)/(2*pdg4621) - exp(-pdg1464)/(2*pdg4621) |
2103023049:
4878728014:
|
2103023049:
4878728014:
|
|
|
24
|
multiply expr 1 by expr 2 |
-
4166155526; locally 7222556:
\({\rm sech}\ x = \frac{2}{\exp(x)+\exp(-x)}\)
\(\operatorname{sech}{\left(pdg_{1464} \right)} = \frac{2}{e^{pdg_{1464}} + e^{- pdg_{1464}}}\)
-
4166155526; locally 7222556:
\({\rm sech}\ x = \frac{2}{\exp(x)+\exp(-x)}\)
\(\operatorname{sech}{\left(pdg_{1464} \right)} = \frac{2}{e^{pdg_{1464}} + e^{- pdg_{1464}}}\)
|
|
-
3868998312; locally 5395954:
\({\rm sech}^2\ x = \frac{4}{\left(\exp(x)+\exp(-x)\right)^2}\)
\(\operatorname{sech}^{2}{\left(pdg_{1464} \right)} = \frac{4}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}}\)
|
valid |
4166155526:
4166155526:
3868998312:
|
4166155526:
4166155526:
3868998312:
|
|
|
28
|
declare final expr |
-
5866629429; locally 8702257:
\({\rm sech}^2\ x + \tanh^2(x) = 1\)
\(\tanh^{2}{\left(pdg_{1464} \right)} + \operatorname{sech}^{2}{\left(pdg_{1464} \right)} = 1\)
|
|
|
no validation is available for declarations |
5866629429:
|
5866629429:
|
|
|
14
|
multiply both sides by |
-
5323719091; locally 2016533:
\(i \sinh x = \frac{1}{2i} \left( \exp(-x) - \exp(x) \right)\)
\(pdg_{4621} \sinh{\left(pdg_{1464} \right)} = \frac{- e^{pdg_{1464}} + e^{- pdg_{1464}}}{2 pdg_{4621}}\)
|
-
9885190237:
\(i\)
\(pdg_{4621}\)
|
-
1038566242; locally 3145608:
\(\sinh x = \frac{\exp(x) - \exp(-x)}{2}\)
\(\sinh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}\)
|
LHS diff is (pdg4621**2 - 1)*sinh(pdg1464)
RHS diff is -2*sinh(pdg1464) |
5323719091:
1038566242:
|
5323719091:
1038566242:
|
|
|
7
|
simplify |
-
2762326680; locally 4009221:
\(\cosh^2 x - \sinh^2 x = \frac{1}{4}\left( \exp(2x)+1+1+\exp(-2x) - \left(\exp(2x)-1-1+\exp(-2x)\right) \right)\)
\(- \sinh^{2}{\left(pdg_{1464} \right)} + \cosh^{2}{\left(pdg_{1464} \right)} = 1\)
|
|
-
9413609246; locally 6300507:
\(\cosh^2 x - \sinh^2 x = 1\)
\(- \sinh^{2}{\left(pdg_{1464} \right)} + \cosh^{2}{\left(pdg_{1464} \right)} = 1\)
|
valid |
2762326680:
9413609246:
|
2762326680:
9413609246:
|
|
|
3
|
multiply expr 1 by expr 2 |
-
1038566242; locally 3145608:
\(\sinh x = \frac{\exp(x) - \exp(-x)}{2}\)
\(\sinh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}\)
-
1038566242; locally 3145608:
\(\sinh x = \frac{\exp(x) - \exp(-x)}{2}\)
\(\sinh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}\)
|
|
-
6031385191; locally 7844176:
\(\sinh^2 x = \left(\frac{\exp(x) - \exp(-x)}{2}\right)\left(\frac{\exp(x) - \exp(-x)}{2}\right)\)
\(\sinh^{2}{\left(pdg_{1464} \right)} = \left(\frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}\right)^{2}\)
|
valid |
1038566242:
1038566242:
6031385191:
|
1038566242:
1038566242:
6031385191:
|
|
|
16
|
change variable X to Y |
-
4585932229; locally 4731536:
\(\cos(x) = \frac{1}{2}\left(\exp(i x)+\exp(-i x) \right)\)
\(\cos{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464} pdg_{4621}}}{2} + \frac{e^{- pdg_{1464} pdg_{4621}}}{2}\)
|
-
7453225570:
\(x\)
\(pdg_{1464}\)
-
1716984328:
\(i x\)
\(pdg_{1464} pdg_{4621}\)
|
-
8651044341; locally 6479977:
\(\cos(i x) = \frac{1}{2} \left( \exp(-x) + \exp(x) \right)\)
\(\cos{\left(pdg_{1464} pdg_{4621} \right)} = \frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\)
|
LHS diff is 0
RHS diff is -cosh(pdg1464) + cosh(pdg1464*pdg4621**2) |
4585932229:
8651044341:
|
4585932229:
8651044341:
|
|
|
8
|
declare final expr |
-
9413609246; locally 6300507:
\(\cosh^2 x - \sinh^2 x = 1\)
\(- \sinh^{2}{\left(pdg_{1464} \right)} + \cosh^{2}{\left(pdg_{1464} \right)} = 1\)
|
|
|
no validation is available for declarations |
9413609246:
|
9413609246:
|
|
|
10
|
declare initial expr |
|
|
-
8418527415; locally 5377003:
\(\sin(i x) = i \sinh(x)\)
\(\sin{\left(pdg_{1464} pdg_{4621} \right)} = pdg_{4621} \sinh{\left(pdg_{1464} \right)}\)
|
no validation is available for declarations |
8418527415:
|
8418527415:
|
|
|
22
|
substitute LHS of expr 1 into expr 2 |
-
6404535647; locally 4319733:
\(\cosh x = \frac{\exp(x) + \exp(-x)}{2}\)
\(\cosh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\)
-
2902772962; locally 6831354:
\(\tanh(x) = \frac{\frac{1}{2}\left( \exp(x)-\exp(-x) \right)}{\cosh(x)}\)
\(\tanh{\left(pdg_{1464} \right)} = \frac{\frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}}{\cosh{\left(pdg_{1464} \right)}}\)
|
|
-
5349669879; locally 5313211:
\(\tanh(x) = \frac{ \exp(x)-\exp(-x)}{\exp(x)+\exp(-x)}\)
\(\tanh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}} - e^{- pdg_{1464}}}{e^{pdg_{1464}} + e^{- pdg_{1464}}}\)
|
valid |
6404535647:
error for dim with 6404535647
2902772962:
5349669879:
|
6404535647:
N/A
2902772962:
5349669879:
|
|
|
13
|
LHS of expr 1 equals LHS of expr 2 |
-
4878728014; locally 5823930:
\(\sin(i x) = \frac{1}{2i}\left(\exp(-x) - \exp(x) \right)\)
\(\sin{\left(pdg_{1464} pdg_{4621} \right)} = \frac{- e^{pdg_{1464}} + e^{- pdg_{1464}}}{2 pdg_{4621}}\)
-
8418527415; locally 5377003:
\(\sin(i x) = i \sinh(x)\)
\(\sin{\left(pdg_{1464} pdg_{4621} \right)} = pdg_{4621} \sinh{\left(pdg_{1464} \right)}\)
|
|
-
5323719091; locally 2016533:
\(i \sinh x = \frac{1}{2i} \left( \exp(-x) - \exp(x) \right)\)
\(pdg_{4621} \sinh{\left(pdg_{1464} \right)} = \frac{- e^{pdg_{1464}} + e^{- pdg_{1464}}}{2 pdg_{4621}}\)
|
input diff is 0
diff is pdg4621*sinh(pdg1464) + exp(pdg1464)/(2*pdg4621) - exp(-pdg1464)/(2*pdg4621)
diff is -pdg4621*sinh(pdg1464) - exp(pdg1464)/(2*pdg4621) + exp(-pdg1464)/(2*pdg4621) |
4878728014:
8418527415:
5323719091:
|
4878728014:
8418527415:
5323719091:
|
|
|
20
|
declare initial expr |
|
|
-
4872163189; locally 3867418:
\(\tanh(x) = \frac{\sinh(x)}{\cosh(x)}\)
\(\tanh{\left(pdg_{1464} \right)} = \frac{\sinh{\left(pdg_{1464} \right)}}{\cosh{\left(pdg_{1464} \right)}}\)
|
no validation is available for declarations |
4872163189:
|
4872163189:
|
|
|
17
|
LHS of expr 1 equals LHS of expr 2 |
-
8747785338; locally 7404421:
\(\cos(i x) = \cosh(x)\)
\(\cos{\left(pdg_{1464} pdg_{4621} \right)} = \cosh{\left(pdg_{1464} \right)}\)
-
8651044341; locally 6479977:
\(\cos(i x) = \frac{1}{2} \left( \exp(-x) + \exp(x) \right)\)
\(\cos{\left(pdg_{1464} pdg_{4621} \right)} = \frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\)
|
|
-
6404535647; locally 4319733:
\(\cosh x = \frac{\exp(x) + \exp(-x)}{2}\)
\(\cosh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\)
|
valid |
8747785338:
8651044341:
6404535647:
error for dim with 6404535647
|
8747785338:
8651044341:
6404535647:
N/A
|
|
|
18
|
declare initial expr |
|
|
-
7731226616; locally 3909583:
\({\rm sech}\ x = \frac{1}{\cosh x}\)
\(\operatorname{sech}{\left(pdg_{1464} \right)} = \frac{1}{\cosh{\left(pdg_{1464} \right)}}\)
|
no validation is available for declarations |
7731226616:
|
7731226616:
|
|
|
23
|
multiply expr 1 by expr 2 |
-
5349669879; locally 5313211:
\(\tanh(x) = \frac{ \exp(x)-\exp(-x)}{\exp(x)+\exp(-x)}\)
\(\tanh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}} - e^{- pdg_{1464}}}{e^{pdg_{1464}} + e^{- pdg_{1464}}}\)
-
5349669879; locally 5313211:
\(\tanh(x) = \frac{ \exp(x)-\exp(-x)}{\exp(x)+\exp(-x)}\)
\(\tanh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}} - e^{- pdg_{1464}}}{e^{pdg_{1464}} + e^{- pdg_{1464}}}\)
|
|
-
2121790783; locally 9317216:
\(\tanh^2(x) = \frac{ \left(\exp(x)-\exp(-x)\right)^2}{\left(\exp(x)+\exp(-x)\right)^2}\)
\(\tanh^{2}{\left(pdg_{1464} \right)} = \frac{\left(e^{pdg_{1464}} - e^{- pdg_{1464}}\right)^{2}}{\left(e^{pdg_{1464}} + e^{- pdg_{1464}}\right)^{2}}\)
|
valid |
5349669879:
5349669879:
2121790783:
|
5349669879:
5349669879:
2121790783:
|
|
|
6
|
simplify |
-
8563535636; locally 4001109:
\(\cosh^2 x - \sinh^2 x = \left(\frac{\exp(x) + \exp(-x)}{2}\right)\left(\frac{\exp(x) + \exp(-x)}{2}\right) - \left(\frac{\exp(x) - \exp(-x)}{2}\right)\left(\frac{\exp(x) - \exp(-x)}{2}\right)\)
\(- \sinh^{2}{\left(pdg_{1464} \right)} + \cosh^{2}{\left(pdg_{1464} \right)} = \left(\frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\right)^{2} - \frac{\left(e^{pdg_{1464}} - e^{- pdg_{1464}}\right)^{2}}{4}\)
|
|
-
2762326680; locally 4009221:
\(\cosh^2 x - \sinh^2 x = \frac{1}{4}\left( \exp(2x)+1+1+\exp(-2x) - \left(\exp(2x)-1-1+\exp(-2x)\right) \right)\)
\(- \sinh^{2}{\left(pdg_{1464} \right)} + \cosh^{2}{\left(pdg_{1464} \right)} = 1\)
|
valid |
8563535636:
2762326680:
|
8563535636:
2762326680:
|
|
|
9
|
declare initial expr |
|
|
-
8747785338; locally 7404421:
\(\cos(i x) = \cosh(x)\)
\(\cos{\left(pdg_{1464} pdg_{4621} \right)} = \cosh{\left(pdg_{1464} \right)}\)
|
no validation is available for declarations |
8747785338:
|
8747785338:
|
|
|
5
|
subtract expr 1 from expr 2 |
-
6031385191; locally 7844176:
\(\sinh^2 x = \left(\frac{\exp(x) - \exp(-x)}{2}\right)\left(\frac{\exp(x) - \exp(-x)}{2}\right)\)
\(\sinh^{2}{\left(pdg_{1464} \right)} = \left(\frac{e^{pdg_{1464}}}{2} - \frac{e^{- pdg_{1464}}}{2}\right)^{2}\)
-
8532702080; locally 9245668:
\(\cosh^2 x = \left(\frac{\exp(x) + \exp(-x)}{2}\right)\left(\frac{\exp(x) + \exp(-x)}{2}\right)\)
\(\cosh^{2}{\left(pdg_{1464} \right)} = \left(\frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\right)^{2}\)
|
|
-
8563535636; locally 4001109:
\(\cosh^2 x - \sinh^2 x = \left(\frac{\exp(x) + \exp(-x)}{2}\right)\left(\frac{\exp(x) + \exp(-x)}{2}\right) - \left(\frac{\exp(x) - \exp(-x)}{2}\right)\left(\frac{\exp(x) - \exp(-x)}{2}\right)\)
\(- \sinh^{2}{\left(pdg_{1464} \right)} + \cosh^{2}{\left(pdg_{1464} \right)} = \left(\frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\right)^{2} - \frac{\left(e^{pdg_{1464}} - e^{- pdg_{1464}}\right)^{2}}{4}\)
|
valid |
6031385191:
8532702080:
8563535636:
|
6031385191:
8532702080:
8563535636:
|
|
|
4
|
multiply expr 1 by expr 2 |
-
6404535647; locally 4319733:
\(\cosh x = \frac{\exp(x) + \exp(-x)}{2}\)
\(\cosh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\)
-
6404535647; locally 4319733:
\(\cosh x = \frac{\exp(x) + \exp(-x)}{2}\)
\(\cosh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\)
|
|
-
8532702080; locally 9245668:
\(\cosh^2 x = \left(\frac{\exp(x) + \exp(-x)}{2}\right)\left(\frac{\exp(x) + \exp(-x)}{2}\right)\)
\(\cosh^{2}{\left(pdg_{1464} \right)} = \left(\frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\right)^{2}\)
|
valid |
6404535647:
error for dim with 6404535647
6404535647:
error for dim with 6404535647
8532702080:
|
6404535647:
N/A
6404535647:
N/A
8532702080:
|
|
|
1
|
declare initial expr |
|
|
-
6404535647; locally 4319733:
\(\cosh x = \frac{\exp(x) + \exp(-x)}{2}\)
\(\cosh{\left(pdg_{1464} \right)} = \frac{e^{pdg_{1464}}}{2} + \frac{e^{- pdg_{1464}}}{2}\)
|
no validation is available for declarations |
6404535647:
error for dim with 6404535647
|
6404535647:
N/A
|
|
Physics Derivation Graph: Steps for hyperbolic trigonometric identities
Clicking on the step index will take you to the page where you can edit that step.
