List of top Mathematics Questions on Properties of Inverse Trigonometric Functions asked in MHT CET

Considering only principal values, the value of $\tan(\sin^{-1}(\frac{3}{5})-2 \cos^{-1}(\frac{2}{\sqrt{5}}))$ is}

If $y = \operatorname{cosec}^{-1} \left[ \frac{\sqrt{x}+1}{\sqrt{x}-1} \right] + \cos^{-1} \left[ \frac{\sqrt{x}-1}{\sqrt{x}+1} \right]$, then $\frac{dy}{dx} =$

$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$, then the values of $x$ are