use this Pythagorean identity ...
(1+ tan x)^2 - sec^2 x = 2 tan x
(1 + tan x) (1 + tan x) - sec^2 x
= 1 + 2 tan x + tan^2 x + 1 - sec^2 x
= 1 + (2 sin x/cos x) + (sin^2 x/cos^2 x) - (1/cos^2 x)
= 1 + (2 sin x/cos x) + (sin^2 x - 1/cos^2 x)
= 1 + (2 sin x/cos x) + (sin^2 x - 1/sin^2 x - 1)
i cancel out the sin^2 x - 1 and i`m left with
1 + (2 sin x/cos x) which is close to 2 tan x
but how do i get rid of the one? any help will be appreciated.