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  4. If cos(sin-1 (2/5)+cos-1 x ) = 0, then x is equal to

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Q. If $cos\left(sin^{-1} \frac{2}{5}+cos^{-1}\,x \right) = 0$, then $x$ is equal to

Inverse Trigonometric Functions

Solution:

$cos\left(sin^{-1} \frac{2}{5}+cos^{-1}\,x \right) = 0$
$\Rightarrow sin^{-1} \frac{2}{5}+cos^{-1}\,x = cos^{-1}\,0 = \frac{\pi}{2}$
$\Rightarrow sin^{-1} \frac{2}{5}+\frac{\pi }{2} -sin^{-1}\,x = \frac{\pi }{2}$
$\Rightarrow sin^{-1}\,x = sin^{-1}\left(\frac{2}{5}\right)$
$\Rightarrow x = \frac{2}{5}$