Question

\(\tan 3A - \tan 2A \cdot \tan A\) is equal to:

• A. \(\tan 3A - \tan 2A - \tan A\)
• B. \(\tan 3A + \tan 2A + \tan A\)
• C. \(\tan 3A \cdot \tan 2A - \tan A\)
• D. None of these

Hint:

When working with complex trigonometric identities, always check for simplifications using standard formulas before making a conclusion. Not every trigonometric equation has a simple, direct solution.

Answer 1

The Correct Option is D

The process begins with expanding the trigonometric expressions \( \tan(3A) \), \( \tan(2A) \), and \( \tan(A) \). Utilizing trigonometric identities for \( \tan(3A) \) and \( \tan(2A) \): \[\n\tan(3A) = \frac{3\tan(A) - \tan^3(A)}{1 - 3\tan^2(A)}\n\] \[\n\tan(2A) = \frac{2\tan(A)}{1 - \tan^2(A)}\n\] Substitution into the original expression does not lead to any of the provided answer choices. Hence, the correct response is (4) None of these.