Question

If $t={\sin }^{-1}{2}^s$, then $\frac{ds}{dt}$ is equal to

• A. $\frac{\log 2}{\sqrt{1-t^2}}$
• B. $\frac{sint}{\log 2}$
• C. $\frac{\cot t}{\log 2}$
• D. $\frac{tant}{\log 2}$

Answer 1

The correct option is C $\frac{\cot t}{\log 2}$

Given, $t={\sin }^{-1}{2}^s$

Therefore, $\sin t=2^s$
$\cos tdt=2^s\log 2ds$
$\cos tdt=\sin t\log 2ds$
$\frac{\cot t}{\log 2}=\frac{ds}{dt}$