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

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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