Question

If $coshx=sec\alpha$ then $cosechx$ =

• A. $sin\alpha$
• B. $cos\alpha$
• C. $tan\alpha$
• D. $cot\alpha$

Answer 1

Answer: (D)

$cot\alpha$

$\sinh x=\frac{e^x-e^{-x}}{2}$

$\cosh x=\frac{e^x+e^{-x}}{2}$

${\sinh }^{2}x={\cosh }^{2}x-1$

${\sinh }^{2}x={\sec }^2\alpha -1={\tan }^2\alpha$

$\Rightarrow \sinh x=\tan \alpha$

$cosechx=\frac{1}{\sinh x}=\cot \alpha$