Решите уравнение2(cos^3x+sin^3x)=2,5(cosx+sinx)

Question

Решите уравнение
2(cos^3x+sin^3x)=2,5(cosx+sinx)

Answer 1

2(cos³x+sin³x)=2.5(cosx+sinx);
2(cosx+sinx)(cos²x-cosxsinx+sin²x)=2.5(cosx+sinx);
2-sin2x=2.5;
sin2x=-1/2;
2x=(-1)ⁿ(-π/6)+nπ;n∈Z;
x=(-1)ⁿ(-π/12)+nπ/2;n∈Z.