Question

If sin⁻¹ x − cos⁻¹ x = `pi/6` , then x = 

Options

• `1/2`

• `sqrt3/2`

• `-1/2`

• none of these

Answer 1

(b) `sqrt3/2`

We know that 

\[\sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2}\]
\[\therefore \sin^{- 1} x - \cos^{- 1} x = \frac{\pi}{6}\]
\[ \Rightarrow \frac{\pi}{2} - \cos^{- 1} x - \cos^{- 1} x = \frac{\pi}{6}\]
\[ \Rightarrow - 2 \cos^{- 1} x = \frac{\pi}{6} - \frac{\pi}{2}\]
\[ \Rightarrow - 2 \cos^{- 1} x = - \frac{\pi}{3}\]
\[ \Rightarrow \cos^{- 1} x = \frac{\pi}{6}\]
\[ \Rightarrow x = \cos\frac{\pi}{6}\]
\[ \Rightarrow x = \frac{\sqrt{3}}{2}\]