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Question

Question: The value of \(\frac{e^{2\theta} - 1}{e^{2\theta} + 1}\) is....

The value of e2θ1e2θ+1\frac{e^{2\theta} - 1}{e^{2\theta} + 1} is.

A

cothθ\coth{}\theta

B

coth2θ\coth{}2\theta

C

tanhθ\tanh{}\theta

D

tanh2θ{\tan h}{}2\theta

Answer

tanhθ\tanh{}\theta

Explanation

Solution

e2θ12eθ=sinhθ\frac{e^{2\theta} - 1}{2e^{\theta}} = {\sin h}\theta

e2θ+12eθ=coshθ\frac{e^{2\theta} + 1}{2e^{\theta}} = {\cos h}\theta

e2θ1e2θ+1=tanhθ\frac{e^{2\theta} - 1}{e^{2\theta} + 1} = {\tan h}\theta.