Evaluate: sin [\pi/3-\sin^{-1}(1/2)]

CBSE Class 12 Math 2008 Solved Paper

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Question : 2

Total: 29

Evaluate: sin [

π

3

−sin−1(

1

2

)]

Solution:

We know that the domain and range of the principal value branch of function sin−1 is defined as:
sin−1 " [- 1 , 1] → [−

π

2

,

π

2

]
∴ sin [

π

3

−sin−1(−

1

2

)] = sin [

π

3

−(−

π

6

)]
= sin [

π

3

+

π

6

]
= sin [

π

2

]
= 1

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