Write everything in terms of #sin# and #cos# using these basic identities:
#tanx=sinx/cosx#
#cscx=1/sinx#
Now, rewrite the whole problem:
#LHS=color(red)tanx*color(blue)cscx*color(green)cosx#
#color(white)(LHS)=color(red)(sinx/cosx)*color(blue)(1/sinx)*color(green)(cosx/1)#
#color(white)(LHS)=(color(red)sinx*color(green)cosx)/(color(red)cosx*color(blue)sinx)#
#color(white)(LHS)=(cancelcolor(red)sinx*color(green)cosx)/(color(red)cosx*cancelcolor(blue)sinx)#
#color(white)(LHS)=color(green)cosx/color(red)cosx#
#color(white)(LHS)=cancelcolor(green)cosx/cancelcolor(red)cosx#
#color(white)(LHS)=1#
#color(white)(LHS)=RHS#