Question

Solve: $\cos \left({\sin }^{-1}x\right)=\frac{1}{6}$

Answer 1

$$\begin{gathered} \cos \left({\sin }^{-1}x\right)=\frac{1}{6} \\ \Rightarrow \cos \left({\cos }^{-1}\sqrt{1-x^2}\right)=\frac{1}{6} \\ \Rightarrow \sqrt{1-x^2}=\frac{1}{6} \\ \Rightarrow 1-x^2=\frac{1}{36} \\ \Rightarrow 1-\frac{1}{36}=x^2 \\ \Rightarrow x^2=\frac{35}{36} \\ \Rightarrow x=\pm \frac{\sqrt{35}}{6} \end{gathered}$$