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Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 22

Answers (1)

Answer: $\frac{4}{5}$

Given: $\cos ^{2}\left(\frac{1}{2} \cos ^{-1} \frac{3}{5}\right) \\$

Hint: $\cos 2 x=2 \cos ^{2} x-1$

Solution:

$\text { Let, } y=\cos ^{-1}\left(\frac{3}{5}\right)\\$

$\cos y=\frac{3}{5} \\$
$\text { Now, } \cos ^{2}\left(\frac{1}{2} \cos ^{-1} \frac{3}{5}\right)=\cos ^{2}\left(\frac{1}{2} y\right) \\$

$=\frac{\cos y+1}{2} \quad\left[\therefore \cos 2 x=2 \cos ^{2} x-1\right] \\$

$=\frac{\frac{z}{5}+1}{2} \\$

$=\frac{\frac{8}{5}}{2} \\$

$=\frac{4}{5}$

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