Math Problem Statement
(sin(2x) + cos(2x))2
Solution
To simplify the expression , we can use trigonometric identities and algebraic expansion.
First, let's expand the square of the binomial:
Next, we apply the Pythagorean identity, which states that :
Thus, the expression simplifies to:
Using the double angle identity for sine, which is , we can further simplify:
Therefore, the simplified form of the expression is:
Summary:
The expression simplifies to .
Do you have any questions or would you like more details?
Here are some related questions to explore further:
- What are the Pythagorean identities in trigonometry?
- How do you use trigonometric identities to simplify expressions?
- What is the double angle formula for sine?
- How can you derive the double angle formulas from the sum formulas?
- What are some applications of trigonometric identities in calculus?
- How can trigonometric identities be used to solve trigonometric equations?
- What is the relationship between trigonometric functions and complex numbers?
- How do you prove trigonometric identities?
Tip: Practicing different trigonometric identities helps in solving complex trigonometric equations more easily.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Trigonometric Identities
Pythagorean Identity
Double Angle Formulas
Formulas
Pythagorean identity
Double angle formula for sine
Theorems
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Suitable Grade Level
Grades 10-12