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

Question

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

Smart Achievers · Accepted Answer

(2)

Ans. $\frac{2}{5}$

Explanation:

We have,

$\cos (\sin^{- 1} \frac{2}{5} + \cos^{- 1} x) = 0$

$\Rightarrow$ $\sin^{- 1} \frac{2}{5} + \cos^{- 1} x = \cos^{- 1} 0$

$\Rightarrow$ $\sin^{- 1} \frac{2}{5} + \cos^{- 1} x = \frac{π}{2}$

$\Rightarrow$ $\cos^{- 1} x = \frac{π}{2} - \sin^{- 1} \frac{2}{5}$

$\Rightarrow$ $\cos^{- 1} x = \cos^{- 1} \frac{2}{5}$ $(∵ \cos^{- 1} x + \sin^{- 1} x = \frac{π}{2})$

$∴$ $x = \frac{2}{5}$

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