Question:
$(\cot A - \cos A)/(\cot A + \cos A) - (\csc A - 1)/(\csc A + 1) = ?$
$(\cot A - \cos A)/(\cot A + \cos A) - (\csc A - 1)/(\csc A + 1) = ?$
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Converting terms to $\sin$ and $\cos$ often reveals common factors.
Updated On: Jun 26, 2026
- 0
- 1
- $\sqrt{2}$
- -1
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Trigonometric identities and simplification.
Step 2: Analysis
Simplify the first term: $\frac{\frac{\cos A}{\sin A} - \cos A}{\frac{\cos A}{\sin A} + \cos A} = \frac{\cos A(\frac{1}{\sin A} - 1)}{\cos A(\frac{1}{\sin A} + 1)}$.
Step 3: Calculation
This simplifies to $\frac{\csc A - 1}{\csc A + 1}$.
The expression becomes: $\frac{\csc A - 1}{\csc A + 1} - \frac{\csc A - 1}{\csc A + 1} = 0$.
Step 4: Conclusion
The value of the expression is 0. Final Answer: (A)
Trigonometric identities and simplification.
Step 2: Analysis
Simplify the first term: $\frac{\frac{\cos A}{\sin A} - \cos A}{\frac{\cos A}{\sin A} + \cos A} = \frac{\cos A(\frac{1}{\sin A} - 1)}{\cos A(\frac{1}{\sin A} + 1)}$.
Step 3: Calculation
This simplifies to $\frac{\csc A - 1}{\csc A + 1}$.
The expression becomes: $\frac{\csc A - 1}{\csc A + 1} - \frac{\csc A - 1}{\csc A + 1} = 0$.
Step 4: Conclusion
The value of the expression is 0. Final Answer: (A)
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