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 = 0 cos2x * (2 * sin3x - sqrt(5)) = 0 1) cos2x = 0 2x = pi/2 + pi*n (n ∈ z) x =  pi/4 + (pi*n)/2 (n ∈ z) 2)2 * sin3x - sqrt(5) = 0 sin3x = sqrt(5)/2 3x = (-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) * cos2x Sinx + sin5x  = 2 * sin ((x+5x)/2) * сos ((5x-x)/2) = 2 * sin3x * cos 2x 2 * sin3x * cos 2x - sqrt(5) * cos2x = 0 cos2x * (2 * sin3x - sqrt(5)) = 0 1) cos2x = 0 2x = pi/2 + pi*n (n ∈ z) x =  pi/4 + (pi*n)/2 (n ∈ z) 2)2 * sin3x - sqrt(5) = 0 sin3x = sqrt(5)/2