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  • Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 57 maths textbook solution

Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 57 maths textbook solution

Answers (1)

Answer:  \frac{5 \pi}{6}

Given:

2 \sec ^{-1} 2+\sin ^{-1}\left(\frac{1}{2}\right)

Hint: Try to convert or find the values of

\sin ^{-1}\left(\frac{1}{2}\right), \sec ^{-1}(2)

Solution:   

\begin{aligned} 2 \sec ^{-1} 2+\sin ^{-1}\left(\frac{1}{2}\right) &=2 \sec ^{1}\left(\sec \frac{\pi}{3}\right)+\sin ^{-1}\left(\sin \frac{\pi}{6}\right) \\ &=2 \times \frac{\pi}{3}+\frac{\pi}{6} \\ &=\frac{5 \pi}{6} \end{aligned}

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