How Does Projectile Angle Affect Range in Physics?

[Questions999]

Galileo showed that, if air resistance is neglected, the ranges for projectiles whose angles of projection exceed or
fall short of 45 degree by the same amount are equal. Prove Galileo’s result.
Answer in my textbook : set θ=45+ - ∂ (I understand this)
Now comes the weird part R = [(v0^2)*sin(90-2∂ ]/g=[V0^2*cos(+-2∂ )]/g.. What formula is this,and how is it transformed this way?

since cos2∂ =cos(-2∂ )
Now we have R(45+θ)=R(45-θ) ..how about this one?How did we get these?

 

[voko]

You need the formula for range given the magnitude of initial velocity and its angle with the horizontal. Do you have it? If not, you will have to derive it from other equations that you have.

 

[Questions999]

I have them but I don't know how to relate them :(

 

[voko]

What equations do you have?