Bsinz Solution tan x sec x 2 tan2 x sec2 x 2 sec x tan x

Solution

( tan x + sec x )^2

= tan^2 x + sec^2 x + 2 sec x tan x

tan x = sin x / cos x

sec x = 1/ cos x

so expression of left side becomes

sin^2 x / cos^2 x + 1/ cos^2 x + 2 sin x / cos^2 x

( sin^2 x + 1 + 2 sin x ) / cos^2 x

( sin x +1 )^2 / cos^2 x

( sin x + 1 )^2 / ( 1 - sin^2 x )

= ( sin x +1 ) ( sin x +1 ) / ( 1 - sin x ) ( 1 + sin x )

= ( sin x +1 ) / ( 1 - sin x )

A= 1 , B = 1