Sin²2x=3/4
a) sin2x = -√3/2
2x = (-1)^n*arcsin(-√3/2) + πn, n∈Z
2x = (-1)^(n+1)*arcsin(√3/2) + πn, n∈Z
2x = (-1)^(n+1)*(π/3) + πn, n∈Z
x1 = (-1)^(n+1)*(π/6) + (πn)/2, n∈Z
b) sin2x = √3/2
2x = (-1)^(n)*arcsin(√3/2) + πk, n∈Z
2x = (-1)^(n)*(π/3) + πk, k∈Z
x2 = (-1)(n)*(π/6) + (πk)/2, k∈Z
2) 3cosX + 5sin X/2 + 1 = 0
3*(1 - 2sin^2(x/2) + 5sin(x/2) + 1 = 0
6sin^(x/2) - 5sin(x/2) - 4 = 0
D = 25 + 4*6*4 = 121
a) sin(x/2) = (5 - 11)/12
sin(x/2) = (-1/2)
x/2 =(-1)^(n)* arcsin(-1/2) + πn, n∈z
x/2 = (-1)^(n+1)*(π/6) + πn, n∈Z
x1 = (-1)^(n+1)*(π/3) + πn, n∈z
b) sin(x/2) = (5 + 11)/12
sin(x/2) = 1
x/2 = π/2 + 2πk, k∈Z
x2 = π + 4πk, k∈z