How to rewrite $\cos2x$ in terms of $\frac{1-\sin x}{ 1+\sin x}$

Question

Would you please tell me how to rewrite $\cos2x$ in terms of

$$\frac{1-\sin(x)}{ 1+\sin(x)}$$ I had rewritten $\cos(2x)$ in terms of $\tan(x)$. But no results! I did this job! Here: $$\cos2x=\frac{\cos(x)-\sin(x)}{ \cos(x)+\sin(x) }$$

Answer 1

Hint :

$$\cos(2x) = \cos^2(x) - \sin^2(x)$$

Answer 2

Hint:

If $\dfrac{1-\sin x}{1+\sin x}=y,\sin x=?$

Now use $\cos2x=1-2\sin^2x$