‹ Back to the paper
Choose the correct option.
The equation sin⁻¹ x - cos⁻¹ x = sin⁻¹(1/2) has:
The equation $\sin^{-1} x - \cos^{-1} x = \sin^{-1}\left(\frac{1}{2}\right)$ has:
- aNo solution
- bTwo solutions
- cUnique solution
- dInfinitely many solutions
Answer
Answer
Correct option: c
Answer: (c) Unique solution
Since $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ and $\sin^{-1} x - \cos^{-1} x = \frac{\pi}{6}$, adding gives $\sin^{-1} x = \frac{\pi}{3}$, so $x = \frac{\sqrt{3}}{2}$ only.