Question

Помогите упростить! sin^6a+cos^6+3sin^2a•cos^2a (10бал)

Answer 1

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