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Question
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Solution
\[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\]
\[ \Rightarrow \cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = \cos\left( \frac{\pi}{2} \right)\]
\[ \Rightarrow \sin^{- 1} \frac{2}{5} + \cos^{- 1} x = \frac{\pi}{2}\]
\[ \therefore x = \frac{2}{5} \left[ \because \sin^{- 1} y + \cos^{- 1} y = \frac{\pi}{2} \right]\]
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