prove that 2(sin^6 A + cos^6 A) - 3(sin^4 + cos^4 A) = -1 - Maths -

Question

prove that 2(sin^6 A + cos^6 A) - 3(sin^4 + cos^4 A) = -1

Ashwini Kumar · Accepted Answer

LHS=2sin6A+cos6A-3sin4A+cos4A=2sin2A3+cos2A3-3sin4A+cos4A=2sin2A+cos2Asin2A2-sin2Acos2A+cos2A2-3sin4A+cos4A=2×1sin4A-sin2A cos2A+cos4A-3sin4A+cos4A=2sin4A-2sin2A cos2A+2cos4A-3sin4A-3cos4A=-sin4A-cos4A-2sin2A cos2A=-sin4A+cos4A+2sin2A cos2A=-sin2A2+cos2A2+2sin2A cos2A=-sin2A+cos2A2=-12=-1=RHSHence, proved