Write the value of ^2 (1 2 ^ -1 3 5 ). - Vidyadip

Question

Write the value of $\cos^2\Big(\frac{1}{2}\cos^{-1}\frac{3}{5}\Big).$

✓

Answer

Let $\text{y}=\cos^{-1}\Big(\frac{3}{5}\Big)$
$\Rightarrow\cos\text{y}=\frac{3}{5}$
Now,
$\cos^2\Big(\frac{1}{2}\cos^{-1}\frac{3}{5}\Big)=\cos^{2}\Big(\frac{1}{2}\text{y}\Big)$
$=\frac{\cos\text{y}+1}{2}$ $\big[\because\ \cos2\text{x}=\cos^2\text{x}-1\big]$
$=\frac{\frac{3}{5}+1}{2}$
$=\frac{\frac{8}{5}}{2}$
$=\frac{4}{5}$
$\therefore\ \cos^2\Big(\frac{1}{2}\cos^{-1}\frac{3}{5}\Big)=\frac{4}{5}$

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