Prove that pi - sin^-1 x = sin^-1 x

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{The} \mathrm{result} \mathrm{is} \mathrm{incorrect} \mathrm{and} \mathrm{hence} \mathrm{cannot} \mathrm{be} \mathrm{proved}. \\ \mathrm{It} \mathrm{only} \mathrm{holds} \mathrm{for} \mathrm{x}=1 \\ \mathrm{\pi }-{\sin }^{-1}\mathrm{x}={\sin }^{-1}\mathrm{x} \\ \Rightarrow {\sin }^{-1}\mathrm{x}+{\sin }^{-1}\mathrm{x}=\mathrm{\pi } \\ \Rightarrow 2{\sin }^{-1}\mathrm{x}=\mathrm{\pi } \\ \Rightarrow {\sin }^{-1}\mathrm{x}=\frac{\mathrm{\pi }}{2} \\ \Rightarrow \mathrm{x}=1 \\ \mathrm{Hence} \mathrm{\pi }-{\sin }^{-1}\mathrm{x}={\sin }^{-1}\mathrm{x} \mathrm{is} \mathrm{only} \mathrm{true} \mathrm{for} \mathrm{x}=1. \\ \mathrm{Please} \mathrm{recheck} \mathrm{your} \mathrm{question}. \end{gathered}$$



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