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Show that acosA+bcosB+ccosC=abc/2R^2 using trigonometric identities

Show that acosA+bcosB+ccosC=abc/2R^2 using trigonometric identities

Grade:8

1 Answers

Avinash
52 Points
4 years ago
We all know that a=2RsinA and b=2RsinBand c=2RsinCSo substitute in the given question.2RsinAcosA+2RsinBcosB+2RsinCcosCWe know that 2sinAcosA=sin2A similarly B and CSo R(sin2A+sin2B+sin2C)We know that sin2A+sin2B+sin2C=4sinAsinBsinC(in a triangle)Therefore R(4sinA.sinB.sinC)We know that a=2RsinA and similarly for B,C4R.a/2R×b/2R.c/2RABC/2R^Hence proved

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