Решите уравнение 6 cos x + 5cos (пи на 2-x) = 7

6cosx+5cos (π/2 - x) = 7;

6cosx+5sinx=7;

6cosx=7-5sinx;

36-36sin²x=49-70sinx+25sin²x;

61sin²x-70sinx+13=0; sinx=z; -1≤z≤1;

61z²-70z+13=0;

z₁,₂ = (70⁺₋√ (4900-4*61*13) / 122 = (70⁺₋√1728) / 122 = (70⁺₋41.57) / 122;

z₁ = (70+41.57) / 122=0.914; ⇒

sinx=0.914; x = (-1) ⁿarcsin0.914+πn; n∈Z;

z₂=0.233; ⇒

sinx=0.233; x = (-1) ⁿarcsin0.233+nπ; n∈Z