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Question

The value of sin2 (π18)+sin2(π9)+sin2 (7π18)+sin2 (4π9) is



Your Answer
A

1

Correct Answer
B

2

Your Answer
C

4

Your Answer
D

none of these


Solution

The correct option is B

2


We have,

sin2 (π18)+ sin2 (π9)+sin2(7π18)+sin2 (4π9)=12[1cos(π9)+1cos(2π9)+1cos7π9+1cos8π9]          (  sin2 θ=1cos 2θ2)=12 [4cos(π9)cos(2π9){cos(π7π9)}{cos(π8π9)}]=12 [4cos(π9)cos(2π9)+(2π9)+cos(π9)]=42=2

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