Question:
Evaluate
\[
\tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A =
\]
Evaluate
\[
\tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A =
\]
Show Hint
When simplifying trigonometric expressions with multiple terms, try to group the terms in a way that applies known identities or common factorizations.
Updated On: Jan 27, 2026
- \( \tan A \)
- \( \cot A \)
- \( \tan 2A \)
- \( \cot 2A \)
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The Correct Option is B
Solution and Explanation
Step 1: Analyze the given expression.
We are given the expression \( \tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A \). After simplifying the terms and applying trigonometric identities, we find that the entire expression simplifies to \( \cot A \).
Step 2: Conclusion.
Thus, the correct answer is \( \cot A \), corresponding to option (B).
We are given the expression \( \tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A \). After simplifying the terms and applying trigonometric identities, we find that the entire expression simplifies to \( \cot A \).
Step 2: Conclusion.
Thus, the correct answer is \( \cot A \), corresponding to option (B).
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