Proving Questions leading to 'Hence' solve for x

I have a question to ask, would anyone of you explain to me how to solve this?

1. Prove that (1+cosθ+sin2θ)/(1-cos2θ+sin2θ)=cotθ

I'm able to prove it but,,

Then the following part asks me solve the equation for 0≤θ≤2π

1+sin2θ=3cos2θ

How would you go about doing this? I appreciate your help!

Re: Proving Questions leading to 'Hence' solve for x

Is the first part supposed to be for the numerator?

If not, can you show me your proof :D

For the second part, wait till someone more experienced comes along; however, while you're waiting, here is my attempt at it...

Let

Solve for t...

For

therefore are some solutions. Not 100% on how to solve for 1/2.

Re: Proving Questions leading to 'Hence' solve for x

Probably you made a mistake in the numerator because I think the identity has to be (like terrorsquid already noticed).

You can prove it this way (I use in stead of ):

The method Terrorsquid used is very useful.

For the other solution:

that means: