Solveeit Logo
Login

Question

Question: The value of \(\cos^{- 1}\left( - \sin\frac{7\pi}{6} \right)\) is-...

The value of cos⁡−1(−sin⁡7π6)\cos^{- 1}\left( - \sin\frac{7\pi}{6} \right) is-

A

5π3\frac{5\pi}{3}

B

7π6\frac{7\pi}{6}

C

π3\frac{\pi}{3}

D

None of these

Answer

π3\frac{\pi}{3}

Explanation

Solution

π2−sin⁡−1(−sin⁡(7π6))\frac{\pi}{2} - \sin^{- 1}\left( - \sin\left( \frac{7\pi}{6} \right) \right) = π2+sin⁡−1sin⁡(7π6)\frac{\pi}{2} + \sin^{- 1}{\sin\left( \frac{7\pi}{6} \right)}

= π2−π6\frac{\pi}{2} - \frac{\pi}{6} = π3\frac{\pi}{3}