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  • Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 18

Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 18

Answers (1)

Answer: \frac{3}{5}

Given:

\sin \left(\tan ^{-1} \frac{3}{4}\right)

Hint: Try to solve \tan  function first.

Solution:

\begin{array}{l} \tan ^{-1} x=\sin ^{-1} \frac{x}{\sqrt{1+x^{2}}} \\\\\end{array}

\begin{array}{l} \sin \left(\tan ^{-1} \frac{3}{4}\right)=\sin \left\{\sin ^{-1}\left(\frac{\frac{3}{4}}{\sqrt{1+\frac{9}{16}}}\right)\right\} \\\\ \\\\\end{array}

                                \begin{array}{l} \qquad=\sin \left\{\sin ^{-1}\left(\frac{\frac{2}{4}}{\frac{5}{4}}\right)\right\} \\\\ \\\\\end{array}

                                \begin{array}{l} \\\\ =\sin \left\{\sin ^{-1} \frac{3}{5}\right\} \\\\ =\frac{3}{5}\\\\\end{array}

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