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The equation you provided is:

\[
\frac{12.5\pi}{60} \cos\left(\frac{\pi}{60}x - 2\pi\right) = \frac{\pi}{4.8} \cos\left(\frac{\pi}{60}x - 2\pi\right)
\]

To find the gradient (slope), we can simplify and compare both sides of the equation.

### Step 1: Simplify the equation
First, notice that the cosine terms on both sides are the same, which means we can divide both sides by \(\cos\left(\frac{\pi}{60}x - 2\pi\right)\) as long as \(\cos\left(\frac{\pi}{60}x - 2\pi\right) \neq 0\).

This gives us:

\[
\frac{12.5\pi}{60} = \frac{\pi}{4.8}
\]

### Step 2: Solve for the gradient

Now, let's simplify both fractions:

\[
\frac{12.5\pi}{60} = \frac{12.5}{60} \cdot \pi = \frac{1}{4.8} \cdot \pi = \frac{\pi}{4.8}
\]

So, the equation simplifies to:

\[
\frac{\pi}{4.8} = \frac{\pi}{4.8}
\]

Since both sides are equal, this equation is always true, meaning there isn't a specific slope (gradient) derived from this equation—it holds for all values of \(x\) where the cosine function is defined.

### Conclusion:
The given equation doesn't have a typical gradient like a linear function because it's an identity after simplification. The "gradient" in this context is not applicable since both sides are equal for all \(x\).

Would you like more details, or do you have any questions about this solution?

### Related Questions:
1. What is the meaning of the cosine function in this equation?
2. How do we handle situations where the cosine function equals zero?
3. What is the significance of simplifying trigonometric equations?
4. How can this type of equation relate to real-world problems?
5. What does it mean for two trigonometric expressions to be equal?

### Tip:
Always check if the functions or terms in an equation can be simplified before solving for variables or other properties like the gradient!

Explore the solution to a trigonometric equation involving the cosine function. Learn how to simplify and compare trigonometric expressions to find equalities. Suitable for advanced math students and enthusiasts of trigonometry.

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