hi, hope this helps as a solution:
tanx=sinx/cosx
substitute this in 2cosx=3sinx/cosx
times both sides by cosx
2cos(^2)x=3sinx
cos(^2)x=1-sin(^2)x
sub this in: 2-2sin(^2)x=3sinx
rearrange so 2sin(^2)x+3sinx-2=0
solve as a quadratic 2x^2+3x-2=0
(x+2)(2x-1)=0
sinx=-2 or sinx=0.5
^no solution
x=sin-1(0.5)
x=(1/6)pi or x=(5/6)pi