Question

For the trig equation: 2sin(x)tan(x) = tan(x),

Why can't I just divide both sides by tan(x) and be left to solve only 2sin(x)=1?

Answer 1

I do not see why not.
x = 30 degrees or 180 - 30 etc

Answer 2

Ahh, but then you would lose solutions....
2sin(x)tan(x) = tan(x)
2sinx tanx - tanx = 0
tanx(2sinx - 1) = 0
tanx = 0 or sinx = 1/2

so tanx = 0
x = 0, 180

or

sinx = 1/3
x = 30° , 150°

so x = 0°, 30°, 150°, 180°, 360° in the domain 0 ≤ x ≤ 360°

Answer 3

Okay thanks! Makes sense now