how does 2cosxsec^2x simplify into 2secx?

Question

I'm using MML for trig homework and it's trying to show me an example because I'm not getting this one problem.

The example says that 2cosxsec^2x=2secx and I don't understand how?

Answer 1

Recall that

 

sec(x) = 1/cos(x).

 

Then

 

2 cos(x) sec²(x) = 2 cos(x) / cos²(x) = 2 / cos(x) = 2 sec(x).