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Question

Mathematics Question on Inverse Trigonometric Functions

sin⁡[π6+cos⁡−1(−32)]=\sin \left[ \frac{\pi}{6} +\cos^{-1}\left(- \frac{\sqrt{3}}{2}\right) \right] =

A

-1

B

0

C

1

D

32\frac{\sqrt{3}}{2}

Answer

0

Explanation

Solution

cos⁡−1(−32)=π−cos⁡−1(32)=π−π6=5π6\cos^{-1} \left(- \frac{\sqrt{3}}{2}\right) = \pi- \cos^{-1} \left(\frac{\sqrt{3}}{2}\right) = \pi -\frac{\pi}{6} = \frac{5 \pi}{6}