The given equation from the image is:

$\frac{\cos^2(x)}{7} + \frac{\sin^2(x)}{7} = 8$

We can factor out $\frac{1}{7}$:

$\frac{1}{7}(\cos^2(x) + \sin^2(x)) = 8$

Now, we use the Pythagorean identity $\cos^2(x) + \sin^2(x) = 1$:

$\frac{1}{7}(1) = 8$

Simplifying:

$\frac{1}{7} = 8$

This equation is not true, meaning no real solution exists for $x$ based on this equation, since $\frac{1}{7}$ cannot equal 8.

Would you like further explanation on this? Here are five related questions to think about:

1. What is the Pythagorean identity for sine and cosine?
2. How can you solve other trigonometric equations with different identities?
3. What if the equation had different coefficients—would it have a solution?
4. How are trigonometric identities useful in physics and engineering?
5. What happens when solving complex trigonometric equations in calculus?

Tip: Always double-check the identities you use, as they simplify many trigonometric expressions.