Question

If f(x) = $si{n}^{-1}\left(sinx\right)+co{s}^{-1}\left(sinx\right)and\varphi \left(x\right)=f\left(f\right(f\left(x\right)\left)\right),then{\varphi }^{\prime }\left(x\right)$ is equal to

• A. 1
• B. sin x
• C. None of these

Answer 1

The correct option is C 0
$f\left(x\right)=\frac{\pi }{2}\left(aconstantfunction\right)$
$\Rightarrow {\varphi }^{\prime }\left(x\right)=0$