sin^-1 x - cos^-1 x = pi/6

We have, \sin^{- 1} x - \cos^{- 1} x = \frac{π}{6} \Rightarrow \sin^{- 1} x + \cos^{- 1} x - 2 \cos^{- 1} x = \frac{π}{6} \Rightarrow \frac{π}{2} - 2 \cos^{- 1} x = \frac{π}{6} \Rightarrow 2 \cos^{- 1} x = \frac{π}{2} - \frac{π}{6} \Rightarrow 2 \cos^{- 1} x = \frac{3 π - π}{6} \Rightarrow 2 \cos^{- 1} x = \frac{2 π}{6} \Rightarrow \cos^{- 1} x = \frac{π}{6} \Rightarrow x = \cos \frac{π}{6} = \frac{\sqrt{3}}{2}

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