Hello

The equation g÷ 2u^2cos^2theta is used to solve Projectile Motion Problems to make make that equation represents Equation of Parabola

Check the Derivation here

Let projectile is thrown with a initial velocity u at an angle theta there with horizontal.

U=uxi+yuk

Ux=ucos theta

Uy=usin theta

Neglecting air resistance

Along x direction

S=ut+1/2at^2

Distance covered by projectile = velocity time

t=X(x)/ucos theta ----------(1)

Along y direction

S=ut+1/2at^2

y=usin theta × t-1/2gt^2 ---------(2)

Substituting (1) in (2)

y= usin theta × x/ucos theta - 1/2 g (x/ucos theta)^2

y=x tan theta - (g/2u^2cos^2theta

Let tan theta =A

-g/2u^2cos^2 theta =B

Y= Ax+Bx^2--------(Parabola)

This equation represents equation of parabola.

Hence path of projectile(Trajectory) is a parabola

Hope this Helps

All the best