Question

The equation $sin^{-1}x - cos^{-1}x = cos^{-1} \left(\frac{\sqrt{3}}{2}\right)$ has

• A. unique solution
• B. no solution
• C. infinitely many solutions
• D. none of these

Answer 1

Answer: (A)

Given, $sin^{-1}x - cos^{-1}x = \frac{\pi}{6} \quad\cdots\left(i\right)$
$sin^{-1}x - cos^{-1}x = \frac{\pi }{2} \quad \cdots \left(ii\right)$
Adding equation $\left(i\right)$ and $\left(ii\right)$, we get
$2sin^{-1} x = \frac{2\pi }{3}$
$\Rightarrow sin^{-1}x = \frac{\pi }{3}$
$\Rightarrow x = sin \frac{\pi }{3} = \frac{\sqrt{3}}{2}$
$\therefore $ Given equation has unique solution.