Question

Evaluate : ${\sin }^{-1}\left(\frac{-1}{2}\right)+2{\cos }^{-1}\left(\frac{-\sqrt{3}}{2}\right)$

• A. $\frac{\pi }{2}$
• B. $\pi$
• C. $\frac{3\pi }{2}$
• D. $noneofthese$

Answer 1

Answer: (C)

$\frac{3\pi }{2}$

Let A$=si{n}^{-1}(-\frac{1}{2})+2co{s}^{-1}(-\frac{\sqrt{3}}{2})$

using $si{n}^{-1}(-x)=-si{n}^{-1}x$ and, $co{s}^{-1}(-x)=\pi -co{s}^{-1}x$

$=-si{n}^{-1}(\frac{1}{2})+2(\pi -co{s}^{-1}(\frac{\sqrt{3}}{2}))$

$=-\frac{\pi }{6}+2(\pi -\frac{\pi }{6})$

$=-\frac{\pi }{6}+\frac{5\pi }{3}$

$A=\frac{9\pi }{6}$

$si{n}^{-1}(-\frac{1}{2})+2co{s}^{-1}(-\frac{\sqrt{3}}{2})$$=\frac{3\pi }{2}$