Sin x+cos x=1/2 найдите sin^4 x+cos^4 x - вопрос №81263101244 от lboik 30.10.2021 15:00

Question

Алгебра: Sin x+cos x=1/2 найдите sin^4 x+cos^4 x

lboik · Answer

(Sinx + Cosx)² = (1/2)²Sin²x + 2SinxCosx + Cos²x = 1/41 + 2SinxCosx = 1/42SinxCosx = - 3/44Sin²xCos²x = 9/162sin²xCos²x = 9/32(Sin²x + Cos²x)² = Sin⁴x + 2Sin²xCos²x + Cos⁴x1 = Sin⁴x + 2Sin²xCos²x + Cos⁴xSin⁴x + Cos⁴x = 1 - 9/32Sin⁴x + Cos⁴x = 23/32...