A) \[\frac{17\pi }{42}-2\]
B) \[-\,2\]
C) \[\frac{-\pi }{21}-2\]
D) none of these
Correct Answer: A
Solution :
[a] \[{{\sin }^{-1}}\sin \left( \frac{22\pi }{7} \right)={{\sin }^{-1}}\sin \left( 3\pi +\frac{\pi }{7} \right)=-\frac{\pi }{7}\] \[{{\cos }^{-1}}\cos \left( \frac{5\pi }{3} \right)={{\cos }^{-1}}\cos \left( 2\pi -\frac{\pi }{3} \right)=\frac{\pi }{3}\] \[{{\tan }^{-1}}\tan \left( \frac{5\pi }{7} \right)={{\tan }^{-1}}\tan \left( \pi -\frac{2\pi }{7} \right)=-\frac{2\pi }{7}\]\[{{\sin }^{-1}}\cos (2)=\frac{\pi }{2}-{{\cos }^{-1}}\cos 2=\frac{\pi }{2}-2\] \[\therefore \]Required value\[=-\frac{\pi }{7}+\frac{\pi }{3}-\frac{2\pi }{7}+\frac{\pi }{2}-2\] \[=\frac{(-18+35)\pi }{42}-2\] \[=\frac{17\pi }{42}-2\]
You need to login to perform this action.
You will be redirected in
3 sec
