Question

If $\cot \left({\cos }^{-1}\frac{3}{5}+{\sin }^{-1}x\right)=0$, find the values of x.

Answer 1

$$\begin{gathered} \cot \left({\cos }^{-1}\frac{3}{5}+{\sin }^{-1}x\right)=0 \\ \Rightarrow {\cos }^{-1}\frac{3}{5}+{\sin }^{-1}x=\cot 0 \\ \Rightarrow {\cos }^{-1}\frac{3}{5}+{\sin }^{-1}x=\frac{\mathrm{\pi }}{2} \\ \Rightarrow {\cos }^{-1}\frac{3}{5}=\frac{\mathrm{\pi }}{2}-{\sin }^{-1}x \\ \Rightarrow {\cos }^{-1}\frac{3}{5}={\cos }^{-1}x\left[\because {\cos }^{-1}x=\frac{\mathrm{\pi }}{2}-{\sin }^{-1}x\right] \\ \Rightarrow x=\frac{3}{5} \end{gathered}$$