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Question

If $\sin^{- 1} \frac{x}{5} + {cosec}^{- 1} (\frac{5}{4}) = \frac{π}{2},$ then $x =$

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Solution

We have,
$\begin{array}{l} \sin^{- 1} \frac{x}{5} + {cosec}^{- 1} \frac{5}{4} = \frac{π}{2} \\ \Rightarrow \sin^{- 1} \frac{x}{5} = \frac{π}{2} - {cosec}^{- 1} \frac{5}{4} \\ \Rightarrow \sin^{- 1} \frac{x}{5} = \frac{π}{2} - \sin^{- 1} \frac{4}{5} \end{array}$
$\begin{array}{l} \Rightarrow \sin^{- 1} \frac{x}{5} = \cos^{- 1} \frac{4}{5} \\ \Rightarrow \sin^{- 1} (\frac{x}{5}) = \sin^{- 1} \frac{3}{5} \Rightarrow x = 3 \end{array}$

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