https://file.aiquickdraw.com/mathbot/file/1727109811208g52n8fr4.jpg

The expression you provided is:

\[
1 - \sin^2 \alpha - \cos^2 \alpha
\]

To simplify this, we can start by using the trigonometric identity:

\[
\sin^2 \alpha + \cos^2 \alpha = 1
\]

Substituting this identity into the expression:

\[
1 - \sin^2 \alpha - \cos^2 \alpha = 1 - (\sin^2 \alpha + \cos^2 \alpha) = 1 - 1 = 0
\]

Thus, the simplified form of the expression is:

\[
0
\]

Would you like more details or have any other questions?

### Related Questions:
1. How do we derive the identity \(\sin^2 \alpha + \cos^2 \alpha = 1\)?
2. What other important trigonometric identities should I know?
3. How does this simplification help in solving trigonometric equations?
4. Can this identity be applied in higher-order trigonometric expressions?
5. How do \(\sin^2 \alpha\) and \(\cos^2 \alpha\) relate to the unit circle?

### Tip:
Always keep trigonometric identities handy, as they simplify many problems in trigonometry.

Learn how to simplify the trigonometric expression 1 - sin^2 α - cos^2 α using key identities such as the Pythagorean trigonometric identity. A step-by-step explanation is provided to help students in Grades 9-11 understand the solution process.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation