Math Problem Statement
sec x - sec x sin ^2 c = cos x
Solution
To solve the given equation, let's rewrite it in a more standard form:
Step 1: Factor out on the left side
The left side can be factored as follows:
Step 2: Simplify using a trigonometric identity
We know that , so we can substitute this into the equation:
Step 3: Substitute
Now, replace with :
Simplify the left side:
This is an identity, meaning it is true for all values of where .
Solution
The equation holds for all where , or equivalently:
Would you like further details or clarification on any step?
Here are some additional questions for practice:
- What values of satisfy ?
- How would you solve ?
- What are the properties of and how do they relate to ?
- Can you prove that using the Pythagorean identity?
- How do you solve trigonometric equations involving both and ?
Tip: Always look for trigonometric identities that can simplify expressions before solving the equation.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Trigonometric Identities
Equation Solving
Formulas
sec x = 1 / cos x
1 - sin^2 x = cos^2 x
Theorems
Pythagorean Identity
Suitable Grade Level
Grades 10-12
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