calculate the left side:
cos x / (1+ sin x)
multiply by (1- sinx/1-sinx)
to get
cos x (1-sinx) / (1+sinx)(1-sinx)
simplify the numerator than the denominator to get
cosx - cosx sinx / 1-sin^2x
apply Pythagorean identity to get
cos x - cosx sin x / cos^2 x
which simplifies to
1-sinx/cos x which equal the right side so it is true
