The equation shown in the image is:

$7 \cos^2 x + 7 \sin^2 x = 8$

We can simplify the equation by using the Pythagorean identity:

$\cos^2 x + \sin^2 x = 1$

So, we substitute this into the equation:

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

$7 \times 1 = 8$

This results in:

$7 = 8$

This is clearly a contradiction, meaning that there is no solution for $x$ that satisfies this equation. The equation is not valid in its current form.

Would you like more details or further explanations?

Here are some related questions for deeper exploration:

1. What are the main trigonometric identities used in solving trigonometric equations?
2. How do you determine if a trigonometric equation has no solution?
3. Can this equation be modified or corrected to have a valid solution?
4. What are other applications of the Pythagorean identity in solving equations?
5. How can contradictions in mathematical equations be interpreted?

Tip: Always double-check the form of trigonometric equations for identities that might simplify them.