Алгебра 10 класс

cos^8x+sin^3x=1

Cos^8x+sin^3x=sin^2x+cos^2x

cos^8x-cos^2x=sin^2x-sin^3x

cos^2x (cos^6x-1) = sin^2x (1-sinx)

(1-sinx) (1+sinx) (cos^6x-1) - sin^2x (1-sinx) = 0

(1-sinx) ((1-sinx) (cos^6x-1) - sin^2x) = 0

1-sinx=0 = > sinx=1

(1-sinx) (cos^6x-1) - sin^2x=0

-sin^6x (1-sinx) - sin^2x=0

-sin^2x (sin^4x+sin^5x+1) = 0

-sin^2x=0

sin^4x+sin^5x+1=0

sin^4x (1+sin^x) + 1=0