take tanx as tan(2x/2) which is equal to 2tan(x/2)/1-{tan(x/2)tan(x/2)}.now use tan(x/2) to find sin(x/2) and cos(x/2).

write tanx=tan(x/2+x/2)

apply property of tan(A+B)=tanA+tanB/1-tanAtanB

tanx=2tanx/2/1-tan^2x/2

-4/3=2tanx/2/1-tan^x/2

solve quadrtic and u will get tan x/2=2 and tan x/2=-1/2

neglect -1/2 as

pi/2<x<pi

pi/4<x/2<pi/2

draw right angled triangle

get sinx/2=2/5

and cosx/2=1/5

rate me