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

ConceptProperties of Inverse Trigonometric Functions

#### 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

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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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