Question

Which out of the following is an even function

• A. $\tan hx$
• B. $cosechx$
• C. $\sec hx+\cos hx$
• D. $\tan hx+\cot hx$

Answer 1

Answer: (C)

We know $\sinh x=\frac{e^x-e^{-x}}{2},\cosh x=\frac{e^x+e^{-x}}{2}$
Clearly $\cosh x$ is even and $\sinh x$ is an odd function.
$\therefore$

Function	Type
$\tanh x$	odd
$co\sec hx$	odd
$\sec hx+\cosh x$	even
$\tanh x+\cot hx$	odd