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  4. If sin(sin-1 (1/5)+cos-1x) = 1, then the value of x is

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Q. If $sin\left(sin^{-1} \frac{1}{5}+cos^{-1}x\right) = 1$, then the value of $x$ is

Inverse Trigonometric Functions

Solution:

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