Just a simple calculus question

[Lisa...]

Why does
((v0^2 sin (2a))/2g) + ((v0 cos a)/g) sqrt(v0^2 ((sin^2)a) +hg) equal
((v0^2 sin (2a))/2g) (1+ sqrt(1+((2hg)/(vo^2) (sin^2)a))) ?

 

[Fermat]

Multiply the right-hand term on the lhs by sin(a) and divide the sq root term by sin²(a) to balance out.
Take out the Vo term from inside the sq root and you should have Vo².sin(2a)/2g as a commom factor.

Let me guess: this to find the angle of elevation for maximum range when firing off a cliff of height h, yes ?

 

[Lisa...]

Exactly! Wow thanks a hell of a lot!