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A+B+C =180° THEN VALUE OF COS2A + COS2B + COS2C = ? Pls.. give a proper explanation of the answer..

A+B+C =180° THEN VALUE OF COS2A + COS2B + COS2C = ? Pls.. give a proper explanation of the answer..

Grade:8

1 Answers

Arun
25750 Points
6 years ago
Dear Ritika
 
cos2A + cos2B + cos2C = 2cos(A+B).cos(A-B) + 2cos^2C -1 
=2cos(180-C).cos(A-B) + 2cos^2C -1 
= - 2cosC.cos(A-B) +2cos^2C -1 
= -2cosC(cos(A-B) - cosC) -1 
= -2cosC(cos(A-B) - cos(180-(A+B)) ) -1 
= -2cosC(cos(A-B) + cos(A+B)) -1 
= -2cosC( 2cosA.cosB) -1 
= -4cosAcosBcosC -1
 
Regards
Arun (askIITians forum expert)

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