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If A+B+C=pi then sin2A+sin2B+sin2C=...

If `A+B+C=pi` then `sin2A+sin2B+sin2C=`

A

4 sin A sin B sin C

B

4 cos A cos B cos C

C

2 cos A cos B cos C

D

2 sin A sin B sin C

Text Solution

Verified by Experts

The correct Answer is:
A
`B+C=pi-A`
`implies sin(B+C)=sin(pi-A)=sinA`
`therefore sin2A+sin2B+sin2C`
`=2sinAcosA+2sin(B+C)cos(B-C)`
`=2sinA[cosA+cos(B-C)]`
`=2sinA[cos(B-C)-cos(B+C)]`
`=2sinA[2sinBsinC]`
`=4sinAsinBsinC`
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