Question

The value of $co{s}^{-1}\left(cos\frac{5\pi }{3}\right)+si{n}^{-1}\left(sin\frac{5\pi }{3}\right)$ is

• A. $\frac{\pi }{2}$
• B. $\frac{5\pi }{3}$
• C. $\frac{10\pi }{3}$
• D. $0$

Answer 1

Answer: (D)

$co{s}^{-1}\left(cos\frac{5\pi }{3}\right)+si{n}^{-1}\left(sin\frac{5\pi }{3}\right)$
$=co{s}^{-1}\left\{cos\left(2\pi -\frac{\pi }{3}\right)\right\}+si{n}^{-1}\left\{sin\left(2\pi -\frac{\pi }{3}\right)\right\}$
$=co{s}^{-1}\left\{cos\frac{\pi }{3}\right\}+si{n}^{-1}\left(-sin\frac{\pi }{3}\right)$
$=\frac{\pi }{3}-\frac{\pi }{3}=0$