State all of the exact solutions of the equation sin x tan x

State all of the exact solutions of the equation sin x tan x = sin x in the interval [0, 2pi). Show work.

Solution

sinxtanx = sinx

sinxtanx - sinx =0

Take sinx as common : sinx( tanx -1) =0

sinx =0 --> x = sin^-1(0) =0 , pi

x = 0, pi

tanx -1 =0

tanx = 1

x = tan^-1(1) = pi/4 , pi -pi/4

= pi/4 , 3pi/4

Solution: x = 0 , pi/4 , pi , 3pi/4 in the interval [ 0, 2pi )