If asecα + btanα =1 and a2sec2α −b2tan2α = 5   then 4a2–9b2 =

(asecα+btanα)(asecα−btanα)=5             ⇒asecα−btanα=5            ⇒−btanα−btanα=5-1            ⇒tanα=−2b            ∴asecα+b(−2b)=1            ⇒secα=3a            sec2α−tan2α=1            ⇒9a2−4b2=1                ⇒4a2−9b2=−a2b2