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Find the Values of `Sin(Pi/3 - Sin^(-1) (-1/2))` is Equal to - CBSE (Science) Class 12 - Mathematics

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Question

Find the values of `sin(pi/3 - sin^(-1) (-1/2))` is equal to 

(A) `1/2`

(B) `1/3`

(C) `1/4`

(D) 1

Solution

Let `sin^(-1) (-1/2) = x . " Then " sin x = (-1)/2 = -sin  pi/6  = sin((-pi)/6)`

We know that the range of the principal value branch of `sin^(-1) is [(-pi)/2, pi/2]`

`:. sin^(-1)(-1/2) = (-pi)/6`

`:. sin(pi/3 - sin^(-1) (-1/2)) = sin(pi/3 + pi/6) = sin((3pi)/6) = sin(pi/2) = 1` 

The correct answer is D.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 2: Inverse Trigonometric Functions
Q: 21 | Page no. 48
Solution Find the Values of `Sin(Pi/3 - Sin^(-1) (-1/2))` is Equal to Concept: Properties of Inverse Trigonometric Functions.
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