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  4. The value of cos ( tan -1 cos sin -1 x) ⋅ operatornamecosec( cot -1 sin cos -1 x) is

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Q. The value of $\cos \left(\tan ^{-1} \cos \sin ^{-1} x\right) \cdot \operatorname{cosec}\left(\cot ^{-1} \sin \cos ^{-1} x\right)$ is

Inverse Trigonometric Functions

Solution:

$\operatorname{cosec}\left(\frac{\pi}{2}-\tan ^{-1} \sin \cos ^{-1} x\right)=\sec \left(\tan ^{-1} \sin \left(\frac{\pi}{2}-\sin ^{-1} x\right)\right)=\sec \left(\tan ^{-1} \cos \sin ^{-1} x\right) $
$\therefore \text { product }=1 .$