Question

Упростите выражение:
Sin6a+cos6a+3sin2a*cos2a

Answer 1

$sin^6a+cos^6a+3sin^2acdot cos^2a=(sin^2a)^3+(cos^2a)^3+3sin^2acdot cos^2a=\\=(sin^2a+cos^2a)(sin^4a-sin^2acdot cos^2a+cos^4a)+3sin^2acdot cos^2a=\\=sin^4a+2sin^2acdot cos^2a+cos^4a=(sin^2a+cos^2a)^2=1^2=1$