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

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

Answers (1)

Answer:
  \frac{-\pi }{3}
Hint:
f\! \left ( x \right )=y
f\! ^{-1}\left ( y \right )=x
Given:
Find\: principal\: value\: o\! f \sin ^{-1}\left ( \frac{-\sqrt{3}}{2} \right )
Solution:
Let,\sin ^{-1}\left ( \frac{-\sqrt{3}}{2} \right )= y
\Rightarrow \sin y= \frac{-\sqrt{3}}{2}
\Rightarrow \sin y= -\sin \left ( \frac{\pi }{3} \right )= \sin \left ( \frac{-\pi }{3} \right )
Range\: o\! f\: principal \: value\: o\! f\: \sin ^{-1} is\left ( \frac{-\pi }{2},\frac{\pi }{2} \right )\: and \: \sin \left ( \frac{-\pi }{3} \right )= \frac{-\sqrt{3}}{2}
There\! f\! ore, principal \: value\: o\! f\: \sin ^{-1}\left ( \frac{-\sqrt{3}}{2} \right )is\: \frac{-\pi }{3}

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