Решить уравнение: cosx+cos2x+cos6x+cos7x=0

(cos7x+cosx) + (cos6x+cos2x) = 2cos4x*cos3x+2cos4x*cos2x=2cos4x (cos3x+cos2x) = 2cos4x*2cos (5x/2) * cos (x/2) = 4*cos4x*cos (5x/2) * cos (x/2) = f (x);

f (x) = 0;

cos4x=0;

4x=π/2+πn. n∈Z.

x=π/8+πn/4. n∈Z.

cos (5x/2) = 0;

5x=π+2πm. m∈Z.

x=π/5+2πm/5. m∈Z.

cos (x/2) = 0;

x=π+2πk. k∈Z.