math

First, use the identity cos2A = 1 - 2sin2A. Substituting this in the equation gives us 2cos2Acos2B +2sinAsinB-1 = 1 - 2sin2Acos2B Rearranging the terms gives us 2sin AsinB + cos2Acos2B - 1 = -2sin2Acos2B Combining like terms on the left hand side gives us 2sinAcosBcos2B -1 = -2sin2Acos2B distributing the cos2B gives us 2sinAcosB -1 = -2sin2Acosp2B factorising out a 2sinAcosB on both sides gives us 2sinAcosB -2sinAcosB= -2sin2Acosp2B -2sinAcosB Simplifying the left side gives us -1 = -2sin2Acosp2B Simplifying the right side gives us -1 = -2sin2Acos2B Thus, the equation 2cos2Acos2B +2sinAsinB-1 = cos2Acos2B is proven.