Galileo, in his book Two new sciences, stated that "for elevations which exceed or fall short of `45^(@)` by equal amounts, the ranges are equal. Prove this statement.

Explanation

To prove Galileo's statement that "for elevations which exceed or fall short of 45 degrees by equal amounts, the ranges are equal," we will follow these steps:

### Step 1: Understand the Range Formula
The range \( R \) of a projectile launched at an angle \( \theta \) with an initial velocity \( V \) is given by the formula:
\[ R = \frac{V^2 \sin(2\theta)}{g} \]
where \( g \) is the acceleration due to gravity.
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