Solve the equation `sin^(-1)6x+sin^(-1)6sqrt(3)x=(-pi)/2dot`

Answer

`x= -(1/12)`

Explanation

From the given equation,
$$
\begin{aligned}
&\sin ^{-1} 6 x=-\frac{\pi}{2}-\sin ^{-1} 6 \sqrt{3} x \\
&\Rightarrow \quad \sin \left(\sin ^{-1} 6 x\right)=\sin \left(-\frac{\pi}{2}-\sin ^{-1} 6 \sqrt{3} x\right) \\
&\Rightarrow \quad 6 x=-\cos \left(\sin ^{-1} 6 \sqrt{3} x\right) \\
&\Rightarrow \quad 6 x=-\sqrt{1-108 x^{2}} \\
& \text {. Squaring, we get } \\
...