How do you prove (tany+coty)/cscy=secy?

Please see below.
##(tany+coty)/cscy##
= ##(siny/cosy+cosy/siny)xx1/(1/siny)##
= ##(sinyxxsiny+cosyxxcosy)/(sinycosy)xxsiny##
= ##(sin^2y+cos^2y)/(cancelsinycosy)xxcancelsiny##
= ##1/cosy##
= ##secy##