prove that cos^2 A+ cos^2 B- 2cosAcosBcos(A+B)= sin^2 (A+B)

Asked by  | 30th May, 2012, 04:42: PM

Expert Answer:

LHS: cos2 A + cos2B -2cosAcosBcos(A+B)

= cos2 A+ cos2B-2cosAcosB(cosAcosB-sinAsinB)

=cos2 A+ cos2B-2cos2Acos2B +2cosAcosBsinAsinB

=cos2 A -cos2Acos2B+ cos2B- cos2Acos2B +2cosAcosBsinAsinB

=cos2 A (1-cos2B) +cos2B (1-cos2 A) +2cosAcosBsinAsinB

=cos2 A sin2 B + cos2B sin2A + 2cosAcosBsinAsinB

= sin2 (A+B) = RHS

Answered by  | 31st May, 2012, 10:36: AM

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