Sin^6x+cos^6x+3sin^2xcos^2x sin^2x+cos^2x+сtg^2x решить - вопрос №31593366322222 от gleb101pro 13.01.2020 18:56

Question

Алгебра: Sin^6x+cos^6x+3sin^2xcos^2x sin^2x+cos^2x+сtg^2x решить по

gleb101pro · Answer

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