Sin x+cos x=1/2

Найдите sin^4 x+cos^4 x

(Sinx + Cosx) ² = (1/2) ²

Sin²x + 2SinxCosx + Cos²x = 1/4

1 + 2SinxCosx = 1/4

2SinxCosx = - 3/4

4Sin²xCos²x = 9/16

2sin²xCos²x = 9/32

(Sin²x + Cos²x) ² = Sin⁴x + 2Sin²xCos²x + Cos⁴x

1 = Sin⁴x + 2Sin²xCos²x + Cos⁴x

Sin⁴x + Cos⁴x = 1 - 9/32

Sin⁴x + Cos⁴x = 23/32