Question is proved based and from trigonometry cum algebra.

Let tanx=t now secx=square root over (1+t^2) put in given rel take (c-at )one side and remain. {b× root of (1+t^2) }on other side square on both sides get a qudratic on t , tanalpha , tanbeta are the roots Use sum of roots and product of roots replace them in proving LHS side by expanding tan of alpha +beta finally u gets result