Embibe Experts Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: Exercise

If ${\sin }^{-1}x=y$, then

Let $f\left(x\right)={\sin }^{-1}x+\left|{\sin }^{-1}x\right|+{\sin }^{-1}\left|x\right|$, then $f\text{'}\left(\frac{-1}{\sqrt{2}}\right)=$

If Principal value of the angle ${\tan }^{-1}\left(\sqrt{\frac{1}{3}}\right)=k°$,then $k=$

Let $f\left(x\right)={\sin }^{-1}x+\left|{\sin }^{-1}x\right|+{\sin }^{-1}\left|x\right|$, then value of $f\left(\frac{1}{2}\right)=$

Let $f\left(x\right)={\sin }^{-1}x+\left|{\sin }^{-1}x\right|+{\sin }^{-1}\left|x\right|$, then $f\text{'}\left(\frac{1}{2}\right)=$

${\sin }^{-1}\left(\sin \theta \right)=\theta$, when 

${\cos }^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{7\pi }{5}-\sin \frac{2\pi }{5}\right)\right\}$ is equal to

FInd the solution of ${\cos }^{-1}\left(\frac{\sin x+\cos x}{\sqrt{2}}\right),\frac{5\mathrm{\pi }}{4}<x<\frac{9\mathrm{\pi }}{4}.$