Kindly solve this problem no 15 b in trigonometry

Dear Student, 

 

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

= cosA+ cos2B-2cosAcosB(cosAcosB-sinAsinB)

=cosA+ cos2B-2cos2Acos2B +2cosAcosBsinAsinB

=cosA -cos2Acos2B+ cos2B- cos2Acos2B +2cosAcosBsinAsinB

=cosA (1-cos2B) +cos2B (1-cosA) +2cosAcosBsinAsinB

=cosA sinB + cos2B sin2A + 2cosAcosBsinAsinB

=(cosAsinB+cosBsinA)2               [(a+b)2=a2+b2+2ab]

​​​​​=[sin(A+B)]2

Or

= sin2 (A+B) = RHS

Using cosA+B=cosAcosB-sinAsinBsinA+B=sinAcosB+sinBcosA

Regards

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