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Question

Mathematics Question on Properties of Inverse Trigonometric Functions

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

A

7π6\frac{7 \pi}{6}

B

5π3\frac{5 \pi}{3}

C

5π6\frac{5 \pi}{6}

D

13π6\frac{13\pi}{6}

Answer

5π6\frac{5 \pi}{6}

Explanation

Solution

cos⁡−1(cos⁡(π+π6))=cos⁡−1(cos⁡(−π6))=π−π6=5π6\cos^{-1} \left(\cos\left(\pi + \frac{\pi}{6}\right)\right) = \cos^{-1} \left(\cos\left( - \frac{\pi}{6}\right)\right) = \pi- \frac{\pi}{6} = \frac{5 \pi}{6}