Si:  a = Senx  y   b = Cosx

Halle: a² + b²

The expressions you've provided are:

- \( a = \sin(x) \)
- \( b = \cos(x) \)

You are asked to find \( a^2 + b^2 \).

Let's compute it:

\[
a^2 + b^2 = (\sin(x))^2 + (\cos(x))^2
\]

Using the Pythagorean identity, we know:

\[
(\sin(x))^2 + (\cos(x))^2 = 1
\]

Therefore, the result is:

\[
a^2 + b^2 = 1
\]

Would you like a deeper explanation or have any further questions?

Here are some related questions:
1. What is the Pythagorean identity?
2. How does the Pythagorean identity apply to trigonometry?
3. Can \( a^2 + b^2 \) ever be different from 1 for any values of \( x \)?
4. How are \( \sin(x) \) and \( \cos(x) \) related on the unit circle?
5. What happens to \( a^2 + b^2 \) if we change the functions to \( \tan(x) \) and \( \cot(x) \)?

**Tip:** Memorizing key trigonometric identities can simplify solving many trigonometric equations.

Si:  a = Senx  y   b = Cosx
Halle: a² + b²

Explore how to solve the trigonometric equation a² + b², where a = sin(x) and b = cos(x). Using the Pythagorean identity, this problem shows that a² + b² equals 1. Perfect for high school students learning trigonometric identities and relationships.

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