Math Problem Statement
Using a Pythagorean identity we see that the equation sin(x) + sin2(x) + cos2(x) = 1 is equivalent to the basic equation
Solution
To simplify the given equation using the Pythagorean identity, let's break it down step by step.
Given equation:
Step 1: Use the Pythagorean identity
One of the fundamental trigonometric identities is:
Step 2: Substitute the identity into the equation
Replace with 1:
Step 3: Simplify the equation
Now, subtract 1 from both sides:
Final Answer:
The equation simplifies to .
Would you like further details or have any questions about this?
Here are 5 related questions:
- What are the solutions to in terms of ?
- How is the Pythagorean identity derived?
- Can equal any value other than 1?
- How do you solve for complex values?
- What are other common trigonometric identities that can simplify equations?
Tip: Always remember to look for fundamental identities like the Pythagorean identity when simplifying trigonometric equations!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Pythagorean Identity
Formulas
sin^2(x) + cos^2(x) = 1
Theorems
Pythagorean Theorem in Trigonometry
Suitable Grade Level
Grades 10-12