Question

If ${\sin }^{-1}x=\frac{\pi }{5}x\in [-1,1]$then, the value of ${\cos }^{-1}x$

Answer 1

We have,

${\sin }^{-1}x=\frac{\pi }{5}$

We know that,

${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$

${\cos }^{-1}x=\frac{\pi }{2}-{\sin }^{-1}x$

Now,

${\cos }^{-1}x=\frac{\pi }{2}-\frac{\pi }{5}$

$=\frac{5\pi -2\pi }{10}$

$=\frac{3\pi }{10}$

Hence, this is the answer.