Prove that the horizontal range is same when angle of projection is (i) greater than ` 45^(@)` by certain value and (ii) less than ` 45^(@)` by the same value.

Explanation

To prove that the horizontal range is the same when the angle of projection is greater than \( 45^\circ \) by a certain value and less than \( 45^\circ \) by the same value, we will use the formula for the range of a projectile.

### Step-by-Step Solution:

1. **Define the Angles of Projection**:
Let the angle of projection greater than \( 45^\circ \) be \( \theta_1 = 45^\circ + \alpha \) and the angle of projection less than \( 45^\circ \) be \( \theta_2 = 45^\circ - \alpha \), where \( \alpha \) is a small angle.

2. **Formula for Range**:
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