Question

The equation $si{n}^{-1}x-co{s}^{-1}x=co{s}^{-1}\left(\frac{\sqrt{3}}{2}\right)$ has

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

Answer 1

Answer: (A)

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