Can anyone help with this question?

I have done all of the parts except the last bit, kinda went a bit over my head there :S

There is also this question that I have gotten really stumped with, I have to try and prove the identitiy, we have only covered the first trig identity so far but we have been set this question, so I am not quite sure what I can do :S

$\displaystyle 1+\tan^2\theta=\frac{1}{\cos^2\theta}$