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A+B+C=180 PROVE THAT sin2 A-sin2 B-sin2 C=-2cosAsinBsinC

  • A+B+C=180 PROVE THAT sin2 A-sin2 B-sin2 C=-2cosAsinBsinC

Grade:8

1 Answers

Jayanth Kasaraneni
50 Points
7 years ago
=sin2A-(sin2B+sin2C)
=sin2A-2sin(B+C)cos(B-C)
as B+C=180-A,
=sin2A-2sinAcos(B-C)
[sin2A=2sinAcosA]
=2sinA(cosA-cos(B-C))
=2sinA(-cos(B+C)-cos(B-C))
=-2sinA(2cosBcosC)
=-4sinAcosBcosC

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