Move point E around to change angle theta.
Why does [math]BE=2\cos\left(\theta\right)[/math]?
Why is [math]\angle EAC=2\theta[/math]?
Why does [math]EF=sin\left(2\theta\right)[/math]?
Why does [math]AF=\cos\left(2\theta\right)[/math]?
In question 3 you explained why [math]EF=sin\left(2\theta\right)[/math]. Why is is also true that [math]EF=2\cos\theta\sin\theta[/math]?
Explain why is [math]\cos\left(2\theta\right)+1=2\cos\theta\cos\theta=2cos^2\theta[/math]?