Prove the identity $\sin\theta/(1+\cos\theta)=(1-\cos\theta)/\sin\theta$

Question

I'm stuck on the equation $$\frac{\sin\theta}{1+\cos\theta}=\frac{1-\cos\theta}{\sin\theta}$$

I just can't figure how to start. I need to flip the equation and change the signs but I'm not sure where to start.

Answer 1

$$\dfrac{\sin\theta}{1+\cos\theta}=\dfrac{\sin\theta\left(1-\cos\theta\right)}{\left(1+\cos\theta\right)\left(1-\cos\theta\right)}=\dfrac{\sin\theta\left(1-\cos\theta\right)}{1-\cos^2\theta}=\dfrac{\sin\theta\left(1-\cos\theta\right)}{\sin^2\theta}=\dfrac{1-\cos\theta}{\sin\theta}$$

Answer 2

Hint: Clear the denominators, and use another, very well known trigonometry identity.