Question:
\(\frac{3\tan 15^{\circ} - \tan^3 15^{\circ}}{1 - 3\tan^2 15^{\circ}}\)
\(\frac{3\tan 15^{\circ} - \tan^3 15^{\circ}}{1 - 3\tan^2 15^{\circ}}\)
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\(\tan 3\theta = \frac{3\tan\theta - \tan^3\theta}{1 - 3\tan^2\theta}\).
Updated On: Apr 25, 2026
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Solution and Explanation
Step 1: Understanding the Concept:
Recall the formula: \(\tan 3\theta = \frac{3\tan \theta - \tan^3 \theta}{1 - 3\tan^2 \theta}\).
Step 2: Detailed Explanation:
The given expression is exactly \(\tan(3 \times 15^{\circ}) = \tan 45^{\circ} = 1\).
Step 3: Final Answer:
The value is 1.
Recall the formula: \(\tan 3\theta = \frac{3\tan \theta - \tan^3 \theta}{1 - 3\tan^2 \theta}\).
Step 2: Detailed Explanation:
The given expression is exactly \(\tan(3 \times 15^{\circ}) = \tan 45^{\circ} = 1\).
Step 3: Final Answer:
The value is 1.
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