sinx+sin5x=корень5cos2x

Sinx + sin5x = sqrt(5) * cos2x-------------------------------------Sinx + sin5x  = 2 * sin ((x+5x)/2) * сos ((5x-x)/2) = 2 * sin3x * cos 2x-------------------------------------2 * sin3x * cos 2x - sqrt(5) * cos2x = 0cos2x * (2 * sin3x - sqrt(5)) = 01) cos2x = 02x = pi/2 + pi*n (n ∈ z)x =  pi/4 + (pi*n)/2 (n ∈ z)2)2 * sin3x - sqrt(5) = 0sin3x = sqrt(5)/23x = (-1)^n * arcsin sqrt(5)/2 + pi*n (n ∈ z)x = (-1)^n * (arcsin sqrt(5)/2)/3 + (pi*n)/3 (n ∈ z)P.s. Точно в условии корень из 5 стоит?

Sinx + sin5x = sqrt(5) * cos2xSinx + sin5x  = 2 * sin ((x+5x)/2) * сos ((5x-x)/2) = 2 * sin3x * cos 2x2 * sin3x * cos 2x - sqrt(5) * cos2x = 0cos2x * (2 * sin3x - sqrt(5)) = 01) cos2x = 02x = pi/2 + pi*n (n ∈ z)x =  pi/4 + (pi*n)/2 (n ∈ z)2)2 * sin3x - sqrt(5) = 0sin3x = sqrt(5)/2