If $\sin ^{-1}\left(x-\frac{x^2}{2}+\frac{x^3}{4}-\frac{x^4}{8}+\ldots\right)=\frac{\pi}{6}$, where

Question

If $\sin ^{-1}\left(x-\frac{x^2}{2}+\frac{x^3}{4}-\frac{x^4}{8}+\ldots\right)=\frac{\pi}{6}$, where $|x|<2$, then the value of $x$ is

Professor PC Thomas Classes · Answer

Summing corresponding boundaries strictly structures angle identities leveraging progression equations identifying structural matching.