Correct Answer - Option 2 : unique solution
Concept:
sin-1x + cos-1x = \(\rm \frac{\pi}{2} \)
cos (30∘ ) = \(\rm \frac{\sqrt{3}}{2}\)
Calculation:
Given
⇒ \(\rm sin^{-1}x-cos^{-1}x=\dfrac{\pi}{6}\)
⇒ sin-1x + cos-1x - 2 cos-1x = \(\rm \frac{\pi}{6}\)
⇒ \(\rm \frac{\pi}{2} \)- 2 cos-1x = \(\rm \frac{\pi}{6}\)
⇒ 2 cos-1x = \(\rm \frac{\pi}{2} - \rm \frac{\pi}{6}\)
⇒ cos-1x = \(\rm \frac{\pi}{6}\)
⇒ x = \(\rm \frac{\sqrt{3}}{2}\)
∴ The equation has unique solution.