Kindly solve this problem no 15 b in trigonometry
Dear Student,
Regards
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
=(cosAsinB+cosBsinA)2 [(a+b)2=a2+b2+2ab]
=[sin(A+B)]2
Or
= sin2 (A+B) = RHS
Regards