\(\displaystyle \frac{1-\sin\theta}{\cos\theta}+\frac{\cos\theta}{1-\sin\theta}=2\sec\theta\)

I started with the left side and used the lcm to get...

\(\displaystyle \frac{1-\sin\theta-\sin\theta+\sin^2\theta+\cos^2\theta}{(1-\sin\theta)(\cos\theta)}\)

Then simplified to get...

\(\displaystyle \frac{2-2\sin\theta}{(1-\sin\theta)(\cos\theta)}\)

and finally...

\(\displaystyle \frac{1-\sin\theta}{\cos\theta}\)

I obviously messed something up somewhere can anyone tell me where I went wrong?