Question:
Evaluate \( \cot 16^\circ \cot 44^\circ + \cot 44^\circ \cot 76^\circ - \cot 76^\circ \cot 16^\circ \):
Evaluate \( \cot 16^\circ \cot 44^\circ + \cot 44^\circ \cot 76^\circ - \cot 76^\circ \cot 16^\circ \):
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When working with sums of cotangents, look for symmetry and use trigonometric identities to simplify the expression.
Updated On: May 13, 2025
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The Correct Option is D
Solution and Explanation
We are given the expression \( \cot 16^\circ \cot 44^\circ + \cot 44^\circ \cot 76^\circ - \cot 76^\circ \cot 16^\circ \).
Step 1: Use trigonometric identities and relationships to simplify. Notice that some terms are symmetric.
Step 2: Apply identities for cotangent and simplify the terms. After performing the calculations, the value simplifies to 3.
Thus, the correct answer is 3.
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