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  • Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 6

Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 6

Answers (1)

Answer: \frac{\pi}{2}

Given:

\tan ^{-1} x+\tan ^{-1}\left(\frac{1}{x}\right) \ \ \text \ \ { for } \ \ x>0

Hint:

\tan ^{-1} x+\tan ^{-1}\left(\frac{1}{x}\right)=\tan ^{-1}\left(\frac{x+\frac{1}{x}}{1-x\frac{1}{x}}\right), x>0

Solution:     

\begin{aligned} \tan ^{-1} x+\tan ^{-1}\left(\frac{1}{x}\right) &=\tan ^{-1}\left(\frac{x^{2}+1}{0}\right) \\ &=\tan ^{-1}(\infty) \\ &=\tan ^{-1}\left(\tan \frac{\pi}{2}\right) \\ &=\frac{\pi}{2} \end{aligned}

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