Question

If $si{n}^{-1}\frac{5}{x}+si{n}^{-1}\frac{12}{x}=\frac{\pi }{2}$, then the value of $x$ is _______________.

• A. 10
• B. 12
• C. 13
• D. 14

Answer 1

The correct option is C 13

Given

${\sin }^{-1}\frac{5}{x}+{\sin }^{-1}\frac{12}{x}=\frac{\pi }{2}$

We know that

${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$

$⟹{\cos }^{-1}\frac{5}{x}={\sin }^{-1}\frac{12}{x}$

$⟹{\sin }^{-1}\frac{\sqrt{x^2-5^2}}{x}={\sin }^{-1}\frac{12}{x}$

$⟹\sqrt{x^2-25}=12$

$⟹x^2=144+25$

$⟹x^2=169$

$⟹x=13$