Question

Solve the following equations .
${\sin }^{-1}\frac{5}{x}+{\sin }^{-1}\frac{12}{x}=\frac{\pi }{2}$

Answer 1

${\sin }^{-1}\frac{12}{x}+{\sin }^{-1}\frac{5}{x}=\frac{\pi }{2}{\sin }^{-1}\frac{12}{x}=\frac{\pi }{2}-{\sin }^{-1}\frac{5}{x}\sin \left({\sin }^{-1}\frac{12}{x}\right)=\sin (\frac{\pi }{2}-{\sin }^{-1}\frac{5}{x})\frac{12}{x}=\frac{\sqrt{x^2-25}}{x}144=x^2-25x^2=169x=13$