Question

cos x - 2 sin x/4 * cos x/4 =0

Answer 1

cosx - 2sin(x/4)cos(x/4) = 0
cosx - sin(x/2) = 0
1 - 2sin²(x/2) - sin(x/2) = 0
2sin²(x/2) + sin(x/2) - 1 = 0
sin(x/2) = t
2t² + t - 1 = 0
D = 1 + 4*2*1 = 9
t1 = (- 1 - 3)/4
t1 = - 1
t2 = ( - 1 + 3)/4
t2 = 1/2
1)  sin(x/2) = - 1
x/2 = - π/2 + 2πk, k∈Z
x1 = - π + 4πk, k∈Z
2)  sin(x/2) = 1/2
x/2 = (-1)^(n)*arcsin(1/2) + πn, n∈Z
x/2 = (-1)^(n)*(π/6) + πn, n∈Z
x2 = (-1)^(n)*(π/3) + 2πn, n∈Z