solve`:sin^-1x+sin^-1 2x=pi/3`

Answer

`x= frac{sqrt{3}}{2 sqrt{7}} `

Explanation

ATQ,
$$
\begin{aligned}
&\sin ^{-1}(\mathrm{x})+\sin ^{-1}(2 \mathrm{x})=\pi / 3 \\
&\Rightarrow \sin ^{-1} x+\sin ^{-1}(2 x)=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) \\
&\Rightarrow \sin ^{-1} x-\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)=-\sin ^{-1}(2 x) \\
&\Rightarrow \quad \sin ^{-1}\left(\frac{x}{2}-\frac{\sqrt{3}}{2} \sqrt{1-x^{2}}\right)=\sin ^{-1}(-2 x) \\
&\Rightarrow \quad\left(\frac{x}{2}-\frac{\sqrt{3}}{2} \sqrt{1-x^{2}}\right)=-2 x \\
...