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  4. cos-1( cos(7π/6)) is equal to

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Q. $\cos^{-1}\left(\cos\frac{7\pi}{6}\right)$ is equal to

Inverse Trigonometric Functions

Solution:

$cos^{-1} \left(cos \frac{7\pi}{6}\right) = cos^{-1} \left(cos\left(2\pi -\frac{5\pi}{6}\right)\right) $
$ = cos^{-1} \left(cos\frac{ 5\pi}{6}\right) = \frac{5\pi}{6}$
$ \left[\because cos^{-1} \left(cos\, \theta\right) = \theta {\text{ if}} \,0\le \theta \le \pi\right]$