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LHS=(cosx +sinx tanx)*cosx / sinx secx cosx
=(cos^2 x +sin^2 x) / sinx
=1/sinx=cscx

i think this one is easier to understand :)

because tanx cosx=sinx, secx cosx=1
multiply cos x makes LHS simpler

Yifian: woot that was so simple! thanks!
haha thanks myinninaya :)

got it (: