Question

solve
${\sin }^{-1}x+{\sin }^{-1}2x=\frac{\pi }{3}$ then $x=?$

Answer 1

${\sin }^{-1}x+{\sin }^{-1}2x=\pi /3$

$\theta ={\sin }^{-1}x;\varphi ={\sin }^{-1}2x$.

$\theta +\varphi =\pi /3$

$\varphi =\pi /3-\theta$

$\sin \varphi =\sin (\pi /3-\theta )$

$2x=\sin \frac{\pi }{3}\cos \theta -\cos \frac{\pi }{3}\sin \theta$.

$2x=\frac{\sqrt{3}}{2}\sqrt{1-x^2}-\frac{x}{2}$

$\frac{5x}{2}=\frac{\sqrt{3}\times \sqrt{1-x^2}}{2}$

$25x^2=3(1-x^2)$

$25x^2-3+3x^2=0$

$28x^2=3$

$x^2=3/28$

$x=\pm 3/28$