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  4. If sin-1x- cos-1 x=(π/6), then x is

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Q. If $\sin^{-1}x-\cos^{-1} x=\frac{\pi}{6}, $ then $x$ is

Inverse Trigonometric Functions

Solution:

$sin^{-1}x-cos^{-1} x = \frac{\pi}{6}$
$ \Rightarrow \frac{\pi}{2} - cos^{-1}x-cos^{-1}x = \frac{\pi}{6} $
$ \Rightarrow 2\,cos^{-1} x = \frac{\pi}{2} -\frac{\pi}{6}$
$= \frac{2\pi}{6} -\frac{\pi}{3}$
$\Rightarrow cos^{-1} = \frac{\pi}{6} $
$\therefore x= cos \frac{\pi}{6}$
$ = \frac{\sqrt{3}}{2}$