solve the equation 2cos x=3tan x, for 0°<x<360°

We know that tan x =sin x/cos x,

so we can multiply the whole equation by cos x which gives us => 2cos^2 x =3 sin x

from the trig identity sin^2 (x)+ cos^2 (x)=1, we can sub in cos^2 (x)=1-sin^2(x) => 2(1-sin^2(x)) =3 sin(x)

multiplying through and rearranging, gives us => 2sin^2 (x) +3sin(x) - 2 = 0

then factorise => (2sin x -1)(sin x + 2)=0

which gives us the solutions of => sin x = 0.5 and sin x = -2 we know sin x =-2 is impossible so we disregard it as an answer, and so from sin x=0.5 we get x=30° This is only one answer because in the question it gives us a range from 0° to 360°. because x is positive, we take it away from 180° => 180-30=150 so the solution to the question is x = 30° and 150°