Sin2A+sin2B+sin2C=4sinAsinBsinC
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sin2A + sin 2B +sin2C
= 2 sin(A+B)cos(A-B) + 2sinC cosC
=2sinC cos(A-B)+2sinC cosC
=2sinC (cos(A-b) + cos C)
=2sin C(cos(A-B) - cos(A+B) )
= 2sinC . 2sin A sin B
=4 sinA sin B sin C
= 2 sin(A+B)cos(A-B) + 2sinC cosC
=2sinC cos(A-B)+2sinC cosC
=2sinC (cos(A-b) + cos C)
=2sin C(cos(A-B) - cos(A+B) )
= 2sinC . 2sin A sin B
=4 sinA sin B sin C
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4
sin2a+sin2b+sin2c
2sin(a+b)cos(a-b)+sin2c
2sinccos(a-b)+2sinccosc
2sinc(cos(a-b)+cosc)
2sinc(cos(a-b)+sin(a+b))
2sinc(2sinasinb)
4sinasinbsinc
2sin(a+b)cos(a-b)+sin2c
2sinccos(a-b)+2sinccosc
2sinc(cos(a-b)+cosc)
2sinc(cos(a-b)+sin(a+b))
2sinc(2sinasinb)
4sinasinbsinc
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