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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.1 Question 1 Subquestion (v) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.1 Question 1 Subquestion (v) Maths Textbook Solution.

Answers (1)

Answer:
\frac{-\pi }{4}
Hint:
\cos x= - \cos \left ( 180^{\circ}-x \right )
Given:
Find\: principal\: value\: o\! f \sin^{-1}\left ( \cos \left ( \frac{3\pi }{4} \right ) \right )
Solution:
Let, \sin^{-1}\left ( \cos \left ( \frac{3\pi }{4} \right ) \right )= y
\Rightarrow\sin y = \cos \left ( \frac{3\pi }{4} \right )
\Rightarrow \sin y= \cos \frac{3\pi }{4}= \cos\left ( \pi -\frac{\pi }{4} \right )= - \cos\left ( \frac{\pi }{4} \right )
Principal\: value \: o\! f \cos^{-1}\: is\: \left [ \frac{-\pi }{2},\frac{\pi }{2} \right ]\: and\: -\cos \cos\left ( \frac{\pi }{4} \right ) = \cos \cos\left ( \frac{3\pi }{4} \right )
There\! f\! ore, principal\: value\: o\! f \sin^{-1}\left ( \cos \left ( \frac{3\pi }{4} \right ) \right ) is \frac{-\pi }{4}.

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