https://file.aiquickdraw.com/mathbot/file/17262250546277jyya20h.jpg

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.

Solve for x in the equation: cos²(x)/7 + sin²(x)/7 = 8

Learn how to solve the trigonometric equation cos²(x)/7 + sin²(x)/7 = 8 using the Pythagorean identity. This problem covers key trigonometric concepts and algebraic manipulation. Suitable for students in Grades 10-12.

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