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  • Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 53 maths textbook solution

Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 53 maths textbook solution

Answers (1)

Answer:  -\pi-\cot ^{-1} x\\

Given

\tan ^{-1}\left(\frac{1}{x}\right) \text { for } x<0  in terms of \cot ^{-1} x\

Hint:

\tan ^{-1}\left(\frac{1}{x}\right)=\tan ^{-1}\left(-\frac{1}{x}\right) for x<0

Solution:        

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

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