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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.10 Question 6 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.10 Question 6 Maths Textbook Solution.

Answers (1)

Answer: \frac{1}{5}
Hint: Convert \sin^{-1}x to \cos^{-1}x or vice versa.
Given:\sin\left \{\sin^{-1}\frac{1}{5}+ \cos^{-1}x \right \} = 1
Here, we have to compute x.
Solution:
\! \! \! \! \! \! \! \! \! \sin^{-1} \frac{1}{5}+ \cos^{-1}x = \sin^{-1}1\\ \Rightarrow \sin^{-1} \frac{1}{5}+ \cos^{-1}x = \frac{\pi }{2}\\ \Rightarrow \cos^{-1}x = \frac{\pi }{2} - \sin^{-1} \frac{1}{5} \; \; \; \; (\because \sin^{-1}x+ \cos^{-1}x= \frac{\pi }{2} )\\ \Rightarrow \cos^{-1}x = \cos^{-1}\frac{1}{5}\\ x = \frac{1}{5}
Concept: Properties of inverse trigonometric functions.
Note: Deriving value of basic Trigonometric functions or remember all degrees of basic Trigonometric functions. 

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