Write the value

Question:

Write the value of $\cos \left(2 \sin ^{-1} \frac{1}{2}\right)$.

Solution:

We have, $\cos \left(2 \sin ^{-1} \frac{1}{2}\right)$

$=\cos \left(2 \times \frac{\pi}{6}\right)$

$=\cos \left(\frac{\pi}{3}\right)=\frac{1}{2}$

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