amath問題！

I have answered this question before:
http://hk.knowledge.yahoo.com/question/?qid=7007101502191
(1) L.H.S. = [1–sec(π/2–θ)–cot (2π-θ)]/[1+sec(3π/2+θ)+cot(π-θ)]
=(1-cscθ+cotθ)/(1+cscθ-cotθ)
=(1-cscθ+cotθ)(1+cscθ+cotθ)/(1+cscθ-cotθ)(1+cscθ+cotθ)
=[(1+cotθ)2-csc2θ]/[(1+cscθ)2-cot2θ] [Since 1+cot2θ=csc2θ]
=[(1+cotθ)2- (1+cot2θ)]/(1+2cscθ+csc2θ-csc2θ+1)
=(1+2cotθ+cot2θ-cot2θ-1)/2(cscθ+1)
= cotθ/ ( 1 + cscθ)
=R.H.S.

[1–sec(π/2–θ)–cot (2π-θ)]/[1+sec(3π/2+θ)+cot(π-θ)]=cotθ/(1+cosecθ)