Question

How do you prove that `cosx/(1-sinx) - 1/cosx = tanx`?

Answer 1

`f(x) = cos x/(1 - sin x) - 1/cos x = [cos ^2 x - (1 - sin x)]/(cos x*(1 - sin x)`

In the numerator of `f(x),` replace

`cos^2 x = 1 - sin^2 x`

Numerator `= 1 - sin^2 x - 1 + sin x =`

`sin x*(1 - sin x)`

`f(x) = (sin x*(1 - sin x))/(cos x*(1 - sin x))= sin x/cos x = tan x.`