Question

Solve : $\sin \left[{\cot }^{-1}\right\{\cos \left({\tan }^{-1}1\right)\left\}\right]=\sqrt{\frac{2}{3}}$

• A. True
• B. False

Answer 1

The correct option is A True

$\sin \left[{\cot }^{-1}\right\{\cos \left({\tan }^{-1}1\right)\left\}\right]$

$=\sin \left\{{\cot }^{-1}\right(\cos \frac{\pi }{4}\left)\right\}$

$=\sin \left({\cot }^{-1}\frac{1}{\sqrt{2}}\right)$

$=\sin \left({\sin }^{-1}\frac{\sqrt{2}}{\sqrt{3}}\right)$

$=\sqrt{\frac{2}{3}}$