sin^6X+cos^6X+3sin^2Xcos^2X sin^2X+cos^2X+сtg^2X Решить по шагам!!

Question

sin^6X+cos^6X+3sin^2Xcos^2X

sin^2X+cos^2X+сtg^2X

Решить по шагам!!

Answer 1

sin^6X+cos^6X+3sin^2Xcos^2X=(sin^2x+cos^2x)(sin^4x+cos^4x-sin^2xcos^2x)+3sin^2xcos^2x=sin^4x+cos^4x+2sin^2xcos^2x=(sin^2x+cos^2x)^2=1^2=1

sin^2X+cos^2X+сtg^2X=1+cos^2x/sin^2x=(sin^2+cos^2x)/sin^2x=1/sin^2x