Question

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

• A. 2
• B. 3
• C. 5
• D. None of these

Answer 1

Answer: (D)

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