Solve cos{2(sin^-1)(-x)}=0

We have : \cos [2 \sin^{- 1} (- x)] = 0 \Rightarrow 2 \sin^{- 1} (- x) = \cos^{- 1} (0) \Rightarrow - 2 \sin^{- 1} x = \cos^{- 1} [\cos (\frac{π}{2})] \Rightarrow - 2 \sin^{- 1} x = \frac{π}{2} \Rightarrow \sin^{- 1} x = - \frac{π}{4} \Rightarrow x = \sin (- \frac{π}{4}) = - \sin (\frac{π}{4}) = - \frac{1}{\sqrt{2}}

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