Question

Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π.

Answer 1

Hello : 
 sin 2x = sin x and 0 ≤ x ≤ 2π.
all solutions : 
2x= x +2kπ    or x= π -x +2kπ ..... k in : Z
x = 2kπ  or : x = π/2 + kπ 
but :
 0 ≤ x ≤ 2π
all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π are : 
k = 0 : x=0    , x= π/2
k=1 : x=2 π    , x=3π/2