Решите уравнение:

Sin2x+2cosx=sinx+1

Sin2x+2cosx=sinx+1

2. sinxcosx+2cosx=sinx+1

2cosx (sinx+1) = sinx+1

2cosx (sinx+1) - (sinx+1) = 0

(sinx+1). (2cosx-1) = 0

a) sinx+1=0, sinx=-1, x=3π/2+2k.π, k∈Z

b) 2cosx-1=0,2cosx=1, cosx=1/2

x=π/3+2k.π, k∈Z

x=2π/3+2k.π, k∈Z

(a. b=0⇔a=0 ∨ b=0)