4син пи/6 * sin (3пи / 2 + x ) + корень из 2 = 0

Question

4син пи/6 * sin (3пи / 2 + x ) + корень из 2 = 0

Answer 1

4sin(π/6) * sin(3π/2 + x) + √2 = 0
4*(1/2)*cosx + √2 = 0
cosx = - √2/2
x = (+ -)arccos(-√2/2) + 2πk, k∈Z
x = (+ -)( π - arccos(√2/2) + 2πk, k∈Z
x = (+ -)( π - π/4) + 2πk, k∈Z
x = (+ -)(3π/4) + 2πk, k∈Z