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  • Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 61 maths textbook solution

Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 61 maths textbook solution

Answers (1)

Answer:  \frac{-\pi}{2}

Given: \tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3})

Hint: Range of

\tan{ }^{-1} \ \ is \ \ \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) ; \frac{\pi}{3} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

Range of

\cot ^{-1} is (0, \pi) ; \frac{5 \pi}{6} \in[0, \pi]

Solution:

\begin{aligned} \tan ^{-1}(\sqrt{3})-\cot ^{-1}(-\sqrt{3}) &=\tan ^{-1}\left[\tan \left(\frac{\pi}{3}\right)\right]-\cot ^{-1}\left(\cot \frac{5 \pi}{6}\right) \\ &=\frac{\pi}{3}-\frac{5 \pi}{6} \\ &=-\frac{\pi}{2} \end{aligned}

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