Evaluate : (2 ^ -1 (2 5 ) ) - Vidyadip

Question

Evaluate : $\cos \left(2 \cos ^{-1}\left(\frac{2}{5}\right)\right)$

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Answer

(d) : $\cos \left(2 \cos ^{-1}\left(\frac{2}{5}\right)\right)=\cos 2 x$, where $x=\cos ^{-1} \frac{2}{5}$ $=2 \cos ^2 x-1=2\left(\frac{2}{5}\right)^2-1 \quad\left(\because \cos x=\frac{2}{5}\right)$
$=\frac{2 \times 4}{25}-1=\frac{8-25}{25}=-\frac{17}{25}$

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