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Q.

If the angles A, B, C of a triangle are in A.P. such  that sin⁡(2A+B)=1/2 then sin⁡(B+2C)=

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a

-12

b

12

c

32

d

12

answer is A.

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Detailed Solution

B=60∘,sin⁡(2A+B)=1/2⇒2A+B=150∘⇒A=45∘,C=75∘so that  B+2C=210∘=180∘+30∘⇒sin⁡(B+2C)=−sin⁡30∘=−1/2
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If the angles A, B, C of a triangle are in A.P. such  that sin⁡(2A+B)=1/2 then sin⁡(B+2C)=