Sin^2(x/2)-cos^2(x/2)=0.5

Question

Sin^2(x/2)-cos^2(x/2)=0.5

Answer 1

Cos²α-sin²α=cos2α

sin²(x/2)-cos²(x/2)=0,5
-(cos²(x/2)-sin²(x/2))=0,5
-cos(2*(x/2))=0,5
cosx=-0,5
x=-+arccos(-0,5)+2πn, n∈Z
x=-+(π-arccos0,5)+2πn, n∈Z
x=-+(π-π/3)+2πn, n∈Z
x=-+(2/3)*π+2πn, n∈Z