1) 1 - cosx = sinxsin(x/20
1 - (1 - 2sin²(x/2)) - sinxsin(x/2) = 0
2sin²(x/2) - 2sin²(x/2)cos(x/2) = 0
2sin²(x/2)*(1 - cos(x/2)) = 0
a) sin²(x/2) = 0
x/2 = πn, n∈Z
x₁ = 2πn, n∈z
b) 1 - cos(x/2) = 0
cos(x/2) = 1
x/2 = 2πk, k∈Z
x₂ = 4πk, k∈Z
2) cos²(3x - π/4) = 3/4
a) cos (3x - π/4) = - √3/2
3x - π/4 = (+ -)arccos(-√3/2) + 2πk, k∈Z
3x - π/4 = (+ -)(π - π/6) + 2πk, k∈Z
3x - π/4 = (+ -)(5π/6) + 2πk, k∈Z
3x = (+ -)(5π/6) + π/4 + 2πk, k∈Z
x₁ = (+ -)(5π/18) + π/12 + 2πk/3, k∈Z
b) cos (3x - π/4) = √3/2
3x - π/4 = (+ -)arccos(√3/2) + 2πn, n∈Z
3x - π/4 = (+ -)(π/6) + 2πn, n∈Z
3x = (+ -)(π/6) + π/4 + 2πn, n∈Z
x₂ = (+ -)(π/18) + π/12 + 2πn/3, n∈Z