Question

cos36⁰÷sin53⁰×sin18⁰÷cos72⁰

Answer 1

perhaps there is a mistake in the given data. It is 54 deg, in place of 53 deg.

$\frac{Cos\ 36\ *\ Sin\ 18}{Sin\ 54\ *\ Cos\ 72}=\frac{Cos\ 36\ *\ Sin\ 18}{Sin\ {(90-36)}\ *\ Cos(90-18)}\\\\=\frac{Cos\ 36\ * Sin\ 18}{Cos\ 36\ *\ Sin18}=1$

If the angle given is 53, then 

$\frac{Cos\ 36\ *\ Sin\ 18}{Sin\ 53\ *\ Cos\ 72}=\frac{Cos\ 36\ *\ Sin\ 18}{Sin\ {(90-37)}\ *\ Cos(90-18)}\\\\=\frac{Cos\ 36\ * Sin\ 18}{Cos\ 37\ *\ Sin18}=\frac{cos\ 36}{Cos\ 37}=1.013\ nearly$