Question

Class XII problem

Find the value of - tan-1(2cos (2sin-1 1/2 ))

Answer 1

$sin^{-1} \frac{1}{2}= \frac{ \pi }{6} \\ \\2sin^{-1} \frac{1}{2}= 2 \times \frac{ \pi }{6} = \frac{ \pi }{3}$

$2cos \frac{ \pi }{3}=2 \times \frac{1}{2} =1$

$tan^{-1}1= \frac{ \pi }{4}$

So answer is $\frac{ \pi }{4}$