2sin x/2 = 1-cosx

Question

2sin x/2 = 1-cosx

Answer 1

Cos(2*x/2) = 1 - 2sin^2(x/2)
2sin(x/2) = 1 - 1 + 2sin^2(x/2)
замена: sin(x/2) = t, t∈[-1;1]
2t^2 - 2t = 0
2t*(t - 1) = 0
t=0, t=1
sin(x/2) = 0,   x/2 = π + 2πk,   x = 2π + 4πk
sin(x/2) = 1,   x/2 = π/2 + 2πk, x = π + 4πk

Answer 2

1-cosx=2*sin(x\2) 
2sin²(x/2)-2sin(x/2)=0 
sin(x/2)(sin(x/2)-1)=0 
a) sin(x/2)=0 
x/2=πn 
x1=2πn 
б) 
sin(x/2)-1=0 
sin(x/2)=1 
x/2=π/2+2πn 
x2=πn+4πn