SOLUTION: Prove: cosh(x)/(1+(sinh(x))^2 = 2e^(x)/(1+e^(2x))

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Question 1180100: Prove:
cosh(x)/(1+(sinh(x))^2 = 2e^(x)/(1+e^(2x))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
cosh%28x%29%2F%281%2B%28sinh%28x%29%29%5E2+%29=+2e%5E%28x%29%2F%281%2Be%5E%282x%29%29

by definition, two basic hyperbolic functions are

sinh%28x%29=%28e%5Ex+-+e%5E%28-x%29%29%2F2 ->sinh%28x%29=%28e%5Ex+-+1%2Fe%5Ex%29%2F2->sinh%28x%29=%28%28e%5E%282x%29+-+1%29%2Fe%5Ex%29%2F2->sinh%28x%29=%28e%5E%282x%29+-+1%29%2F%282e%5Ex%29

and

cosh%28x%29=%28e%5Ex+%2B+e%5E%28-x%29%29%2F2->cosh%28x%29=%28e%5Ex+%2B+1%2Fe%5E%28x%29%29%2F2->cosh%28x%29=%28%28e%5E%282x%29+%2B+1%29%2Fe%5Ex%29%2F2->cosh%28x%29=%28e%5E%282x%29+%2B+1%29%2F%282e%5Ex%29


start with left side, substitute values above

=


=---...simplify


=



=...simplify


=


=1%2F%28%28e%5E%282+x%29+%2B+1%29%2F%282e%5Ex%29+%29


=%282e%5Ex%29%2F%28e%5E%282+x%29+%2B+1+%29=>proven