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  • Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 41 maths textbook solution

Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 41 maths textbook solution

Answers (1)

Answer: \frac{5}{12}

Given:

\tan \left(2 \tan ^{-1} \frac{1}{5}\right)

Hint:

Use formula

Solution:         

\begin{aligned} \tan \left(2 \tan ^{-1} \frac{1}{5}\right) &=\tan \left(\tan ^{-1} \frac{2 \times\left(\frac{1}{5}\right)}{1-\left(\frac{1}{5}\right)^{2}}\right) \\\\ &=\tan \left(\tan ^{-1} \frac{\frac{2}{5}}{\frac{24}{25}}\right) \\\\ &=\frac{5}{12} \end{aligned}

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