SOLUTION: Prove sinh(z)=isin(iz)

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Question 1181956: Prove sinh(z)=isin(iz)
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Prove
sinh%28z%29=i%2Asin%28iz%29
That isn't true.  What's true is

sinh%28z%29=-i%2Asin%28iz%29

Start with right side:

-i%2Asin%28iz%29%22%22=%22%22

-i%2A%28%28e%5E%28i%28iz%29%29-e%5E%28-i%28iz%29%29%29%2F%282i%29%29%29%22%22=%22%22

%22%22=%22%22

matrix%282%2C1%2C%22%22%2C-%28%28e%5E%28-1z%29-e%5E%28-%28-1%29z%29%29%2F%282%29%29%29%22%22=%22%22

-%28%28e%5E%28-z%29-e%5E%28z%29%29%29%2F%282%29%29%29%22%22=%22%22

%28-%28e%5E%28-z%29%2Be%5E%28z%29%29%29%2F%282%29%29%29%22%22=%22%22

%28e%5Ez%2Be%5E%28-z%29%29%2F%282%29%29%29%22%22=%22%22

sinh%28z%29

Edwin