secx - tanx = cosx/1 + sinx
( secx = 1/cosx and tanx = sinx/cosx )
1/cosx - sinx/cosx = cosx/1 + sinx
(1 - sinx )/cosx = cosx /(1+ sinx) *cosx(1+sinx)
(1-sinx )(1+sinx) = cosx^2
(a-b)(a+b) = a^2 - b^2, a =1 and b = sinx
1-sinx^2 = cosx^2 , 1-sinx^2 =1 ⇒
cosx^ 2 =cosx^2