Secx + tanx = cosx / (1-sinx)
Taking LHS
= Secx + Tanx
sec x = 1/cos x and
tan x = sin x / cox x
Putting the values of secx and tanx you will get
= secx + tanx
= 1/cosx + sinx / cosx
By Taking LCM you will get
= (1 + sinx) / cosx
Multiply the numerator and denominator by (1-sinx)
= (1-sinx)(1+sinx) / cosx(1-sinx)
= (1-sin^2 x) / (cos x - sin x cos x)
As 1-sin^2 x = cos^2 x therefore;
= cos^2 x / [cosx (1-sin x)]
Divided numerator and denominator by cos x you will get
= cosx / (1-sin x)