Show that (cosa+cos3a)/(sina+sin3a)=cot2a

This is a rather brute-force way of doing it, only using the very basic identities.refresh the page if the tex hasn't loaded, or view on a computer if viewing on mobile. alternatively see the attachments.  addition identities:         so focusing on the right hand side:     by definition,      so it follows that    using double angle identities:         ======focusing on the  left-hand side, it turns into    cosine and sine double angle identity usage incoming.focusing on denominator: change all the cos2a and sin2a and distribute.    note that sin a can be factored out of the numerator:     expanding out numerator with identities, then factor out cos a afterwards.    since      then        cosine in numerator and denominator cancel out.2 and 4 simplify each other to become 1 and 2 respectively