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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.10 Question 10 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.10 Question 10 Maths Textbook Solution.

Answers (1)

Answer: 1
Hint: Use \tan^{-1}x + \cot^{-1}x= \frac{\pi }{2}
Given: 5\tan^{-1}x + 3\cot^{-1}x= 2\pi
Here, we have to compute x.
Solution:
As we know,\tan^{-1}x + \cot^{-1}x= \frac{\pi }{2}
Therefore,
\Rightarrow \frac{\pi }{2} - \tan^{-1}x = \cot^{-1}x
\Rightarrow 5\tan^{-1}x + 3\cot^{-1}x= 2\pi
\Rightarrow 5 \tan^{-1}x + 3 (\frac{\pi }{2} - \tan^{-1}x ) = 2\pi
\! \! \! \! \! \! \! \! \! {\Rightarrow }5 \tan^{-1}x - 3 \tan^{-1}x = 2\pi - \frac{3\pi }{2}\\ \Rightarrow 2 \tan^{-1}x = \frac{\pi }{2}\\ \Rightarrow \tan^{-1}x = \frac{\pi }{4}\\ \Rightarrow x = \tan \frac{\pi }{4}\\ \therefore x = 1
Concept: Properties of inverse trigonometric functions.
Note: Value of basic Trigonometric functions should be memorised.

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