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B
2sinAcosBsinC
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C
2sinAcosBcosC
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D
2sinAsinBsinC
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Solution
The correct option is B2sinAcosBsinC sin2A−sin2B+sin2C=sin(A+B)sin(A−B)+sin2C(∵sin(A+B)=sin(π−C)=sinC)=sinC(sin(A−B)+sinC)=sinC(sin(A−B)+sin(A+B))=2sinAcosBsinC