Math Problem Statement
seca-1/seca+1=1-cosa/1+cosa
Solution
We are given the following trigonometric equation to solve:
Step 1: Express in terms of
Since , we can substitute this into the equation:
Step 2: Simplify the left-hand side
To simplify, multiply the numerator and denominator by :
Now the equation becomes:
Step 3: Analyze the equation
The left-hand side is , while the right-hand side is . Notice that:
So the right-hand side is the negative of the left-hand side:
Thus, the equation becomes:
Step 4: Solve for
For this equation to hold, the only way for is if:
This implies:
Step 5: Conclusion
The solution to the equation is:
Would you like more details on any step? Here are 5 related questions:
- What is the definition of in trigonometry?
- How can trigonometric identities help simplify complex equations?
- What are the implications of in trigonometry?
- How would the equation change if ?
- How do transformations affect trigonometric identities?
Tip: When simplifying trigonometric equations, always look for basic identities like to help reduce complexity.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Trigonometric Identities
Formulas
sec(A) = 1/cos(A)
cos(A)
Theorems
Trigonometric Identity Simplification
Cosine Value Theorem
Suitable Grade Level
Grades 10-12
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