Question

In ∆abc angle c=90° and cot B=1/√3 then prove cosA×cosB=sinA×sinB

Answer 1

if cot B=1/root3 it means that B=60 so a will be 30 cosA×cosB=cos30×cos60=1/2×root3/2=root3/4
and sinA×sinB=sin30×sin60=root3/2×1/2=root3/4
so cosA×cosB=sinA×sinB
hence proved