The direction of a projectile at a certain instant is inclined at an angle `prop` to the horizontal , after `t` second, it is inclined at an angle `beta`. Prove that the horizontal component of the velocity of the projectile is `("gt")/(tan prop - tan beta)`.

Explanation

To prove that the horizontal component of the velocity of the projectile is given by the formula \( \frac{gt}{\tan \alpha - \tan \beta} \), we can follow these steps:

### Step 1: Understand the Initial Conditions
Let the projectile be at point \( P \) at an initial time \( t = 0 \) with an initial velocity \( u \) inclined at an angle \( \alpha \) to the horizontal.

### Step 2: Resolve the Initial Velocity
The horizontal and vertical components of the initial velocity \( u \) can be expressed as:
- Horizontal component: \( u_x = u \cos \alpha \)
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