Question

Решите уравнение:

Sin2x+2cosx=sinx+1

Answer 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)