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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.10 Question 1 Subquestion (ii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.10 Question 1 Subquestion (ii) Maths Textbook Solution.

Answers (1)

Answer:-1
Hint: Check if there is any relation between\sec ^{-1}x  and \cos^{-1}x . Use inverse trigonometric functions properties to solve.( \therefore \tan^{-1}\frac{1}{x} = - \pi + \cot^{-1}x )
Given: \sin\left (\tan^{-1}x+ \tan^{-1}\frac{1}{x} \right ) f\! or\: x < 0
Solution: Let replace \tan^{-1}\frac{1}{x}  by  (- \pi + \cot^{-1}x) , x < 0
Now,\sin\left (\tan^{-1}x+ \tan^{-1}\frac{1}{x} \right )
\Rightarrow \sin\left (\tan^{-1}x- \pi + \cot^{-1}x \right )
Again by property,  \tan^{-1}x+ \cot^{-1}x = \frac{\pi }{2}
\! \! \! \! \! \! \! \! \! \! = \sin\frac{\pi }{2}- \pi \\ = \sin-\frac{\pi }{2}\\ = - 1
Concept: Properties and relations between inverse trigonometric functions.
Note: Inverse trigonometric functions remember relation between all trigonometric functions. Also, try to remember value of trigonometric functions.  

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