Question

The value of the expression ${\sin }^{-1}\left(\sin \frac{22\pi }{7}\right)+{\cos }^{-1}\left(\cos \frac{5\pi }{3}\right)+{\tan }^{-1}\left(\tan \frac{5\pi }{7}\right)+{\sin }^{-1}\left(\cos 2\right)$ is

• A. $\frac{17\pi }{42}-2$
• B. $-2$
• C. $\frac{-\pi }{21}-2$
• D. $noneofthese$

Answer 1

The correct option is A $\frac{17\pi }{42}-2$

$si{n}^{-1}\left(sin\right(3\pi +\frac{\pi }{7}\left)\right)+co{s}^{-1}\left(cos\right(2\pi -\frac{\pi }{3}\left)\right)+ta{n}^{-1}\left(tan\right(\pi -\frac{2\pi }{7}\left)\right)+\frac{\pi }{2}-2$

$=-\frac{\pi }{7}+\frac{\pi }{3}-\frac{2\pi }{7}+\frac{\pi }{2}-2$

$=\frac{5\pi }{6}-\frac{3\pi }{7}-2$

$=\frac{17\pi }{42}-2$