Math Problem Statement
If A+B = 90°then what’s the value of 1+ cotA/cotB = cosec²A
Solution
Given the condition , we need to find the value of the expression .
Step-by-Step Solution:
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Complementary Angle Relationship: Since , . This implies that is the complementary angle of .
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Cotangent of a Complementary Angle: The cotangent of a complementary angle is: Therefore, .
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Substitute into the Expression: The expression we want to simplify is: Substitute into the expression:
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Simplify the Expression: Notice that: So, the expression simplifies to:
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Use the Pythagorean Identity: The Pythagorean identity for cotangent and cosecant is:
Conclusion:
The value of the expression is equal to .
Would you like any more details or have any other questions?
Related Questions:
- How can the identity be derived?
- What is the relationship between the trigonometric functions of complementary angles?
- How does the Pythagorean identity apply to other trigonometric functions?
- Can you find the value of if ?
- What are some common trigonometric identities involving , , and ?
Tip: Understanding complementary angles and their identities can significantly simplify solving trigonometric problems.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Complementary angles
Trigonometric identities
Formulas
Pythagorean identity: 1 + cot^2 A = csc^2 A
Theorems
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Suitable Grade Level
High school
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