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  4. The value of cos [(1/2) cos -1( cos (-(14 π/5)))] is/are -

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Q. The value of $\cos \left[\frac{1}{2} \cos ^{-1}\left(\cos \left(-\frac{14 \pi}{5}\right)\right)\right]$ is/are -

Inverse Trigonometric Functions

Solution:

$\cos \left[\frac{1}{2} \cos ^{-1} \cos \left(2 \pi+\frac{4 \pi}{5}\right)\right]$
$=\cos \left(\frac{1}{2} \times \frac{4 \pi}{5}\right)=\cos \frac{2 \pi}{5}$
$=\cos \left(\pi-\frac{3 \pi}{5}\right)=-\cos \left(\frac{3 \pi}{5}\right)$
$\& \cos \frac{2 \pi}{5}=\sin \left(\frac{\pi}{2}-\frac{2 \pi}{5}\right)=\sin \left(\frac{\pi}{10}\right)$