证:(cos^6 x )+ (sin^6 x) =[(cos^2 x )]^3+ [(sin^2 x)]^3 =[(cos^2 x )]+ [(sin^2 x)]*[ [(cos^4 x )-[(cos^2 x )(sin^2 x)+[(sin^4x)]=1*{[(cos^2 x )+ (sin^2 x)]^2-3(cos^2x) (sin^2 x) }=1-3(cos^2x) (sin^2 x...