Prove that: 2sin^B + 4cos(A+B)sinAsinB + cos2(A+B) = cos2A - Maths - Trigonometric Functions

Question

Prove that: 2sin^B + 4cos(A+B)sinAsinB + cos2(A+B) = cos2A

Anuradha Sharma · Accepted Answer

Taking LHS, 2sin2B+4cosA+BsinAsinB+cos2A+B=2sin2B+4cosA+BsinAsinB+2cos2A+B-1=2sin2B-1+2cosA+B2sinAsinB+cosA+B=2sin2B-1+2cosA+B2sinAsinB+cosAcosB-sinAsinB=2sin2B-1+2cosA+BcosAcosB+sinAsinB=2sin2B-1+2cosA+BcosA-B=2sin2B-1+2cos2A-sin2B=2cos2A-1=cos2A=RHS