Math Problem Statement
(csc(alpha)+cot(alpha))/tan(alpha)+sin(alpha)= cot(alpha)csc(alpha) Identify the erroneous step(s) (those that are NOT equal to the LHS)
Solution
To identify the erroneous step(s) in the given expression , let's break down the problem step by step.
Given Expression
Step-by-Step Simplification
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Rewrite the given trigonometric identities in terms of and :
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Substitute these identities into the given expression:
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Combine the terms in the numerator:
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Simplify the complex fraction:
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Combine the terms:
Compare with the Right-Hand Side
Now, analyze:
Clearly, these two expressions are not equal, which means the left-hand side cannot be simplified to the right-hand side. Therefore, one of the steps (or the initial equality assumption) must be erroneous.
Error Identification:
The erroneous step is assuming that: is true, since:
Thus, the error lies in the initial assumption itself. The step-by-step simplification shows that the left-hand side and the right-hand side do not match.
Would you like further details on any part of this solution or any other questions? Here are some related questions you might find useful:
- How do you simplify trigonometric expressions?
- What are the common trigonometric identities?
- How do you convert between different trigonometric functions?
- What is the significance of simplifying expressions in trigonometry?
- How can you verify trigonometric identities?
- What is the difference between , , and ?
- How do you handle complex fractions in trigonometry?
- What strategies can you use to solve trigonometric equations?
Tip: Always double-check each step when verifying trigonometric identities to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Trigonometric Identities
Complex Fractions
Formulas
Trigonometric identities involving sine, cosine, cosecant, cotangent, tangent
Theorems
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Suitable Grade Level
High School
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