Math Problem Statement
Solution
Let's match each expression with its equivalent from the options.
1.
- Using the Pythagorean identity: .
- Match: .
2.
- Using the identity: .
- Match: .
3.
- Using the co-function identity: .
- Match: .
4.
- Using the identity: .
- Match: .
5.
- Using the co-function identity: .
- Match: .
6.
- Using the odd function property: .
- Match: .
7.
- Using the even function property: .
- Match: .
Final Matches
Here is the list of expressions and their equivalents:
- →
- →
- →
- →
- →
- →
- →
Would you like a detailed explanation for any of these matches?
Related Questions
- What are other examples of trigonometric identities?
- How do co-function identities work in trigonometry?
- Can you explain the difference between even and odd trigonometric functions?
- How are Pythagorean identities derived in trigonometry?
- What are the applications of trigonometric identities in calculus?
Tip
To remember co-function identities, note that functions like sine and cosine, tangent and cotangent, secant and cosecant are paired such that each function equals its co-function at complementary angles.
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Math Problem Analysis
Mathematical Concepts
Trigonometric Identities
Pythagorean Identities
Co-function Identities
Odd and Even Properties
Formulas
sin^2 u = 1 - cos^2 u
csc^2 u = 1 + cot^2 u
cos(π/2 - u) = sin u
sec^2 u = 1 + tan^2 u
csc(π/2 - u) = sec u
tan(-u) = -tan(u)
cos(-u) = cos(u)
Theorems
Pythagorean Identities
Co-function Identities
Odd and Even Properties
Suitable Grade Level
Grades 10-12
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