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  4. If sin -1 (5/x)+ sin -1 (12/x)=(π/2), then find value of x.

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Q. If $\sin ^{-1} \frac{5}{x}+\sin ^{-1} \frac{12}{x}=\frac{\pi}{2}$, then find value of $x$.

Inverse Trigonometric Functions

Solution:

$\cos ^{-1} \frac{\sqrt{x^{2}-25}}{x}+\sin ^{-1} \frac{12}{x}=\frac{\pi}{2}$
$\sqrt{x^{2}-25}=12$
$x^{2}=169$
$x=13$