Galileo writes that for angles of projection of a projectile at angles $(45 + \theta )$ and $(45 - \theta )$, the horizontal ranges described by the projectile are in the ratio of (if $\theta \le 45)$
$2:1$
$1:2$
$1:1$
$2:3$
Galileo writes that for angles of projection of a projectile at angles $(45 + \theta )$ and $(45 - \theta )$, the horizontal ranges described by the projectile are in the ratio of (if $\theta \le 45)$
For angle $(45^\circ - \theta )$, $R = \frac{{{u^2}\sin (90^\circ - 2\theta )}}{g} = \frac{{{u^2}\cos 2\theta }}{g}$
For angle $(45^\circ + \theta )$, $R = \frac{{{u^2}\sin (90^\circ + 2\theta )}}{g} = \frac{{{u^2}\cos 2\theta }}{g}$