求证(cos^6x)+(sin^6x)=1-3sin^2x+3sin^4x写下左右过程.

Question

求证 (cos^6 x )+ (sin^6 x) = 1 -3sin^2 x + 3sin^4 x
写下左右过程.

Answer 1

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) =
1-3(1-3sin^2 x)(sin^2 x) =
1 -3sin^2 x + 3sin^4 x