Question

Differentiate the following w.r.t.x:
${\sin }^{-1}(2{\cos }^{2}x-1)$

Answer 1

${\sin }^{-1}(2{\cos }^{2}x-1)$

$={\sin }^{-1}\left(\cos 2x\right)$

$={\sin }^{-1}\left(\sin \right(\frac{\pi }{2}-2x\left)\right)$

$=\frac{\pi }{2}-2x$

Now, differentiating it w.r.t x , we get,

$0-2=-2$