Convert cos(x) to cos(2(x/2)) and substitute using a double-angle identity to rearrange the denominator to get 2cos^2(x/2). Then the fraction can be restated as (1/2)sec^2(x/2).
Then apply what you know about the derivative of the tangent....
No. From the usual double angle formula it's from which it follows that .
And since it follows from the compound angle formula that .
From which the correct answer of 2 follows. You are going to continue to struggle with these 'higher level' questions if you don't start extensively reviewing the 'lower level' material that underpins these questions.
I also agree. Totally. But I wanted to validate the method used by the OP. (The Weierstrass substitution is the routine cookbook way that students are taught to do these - using conjugates might, to the OP, look too much like pulling rabbits out of a hat ....)