Question

If \( A, B, C \) are angles of a triangle ABC, then \( \tan 2A + \tan 2B + \tan 2C = \)

• A. \( \tan 2A \tan 3B \tan 2C \)
• B. \( \tan 2A \tan 2B \tan 2C \)
• C. \( \tan A \tan B \tan C \)
• D. \( \tan 3A \tan 2B \tan 2C \)

Hint:

For problems involving trigonometric identities of angles in a triangle, remember the standard identities that relate the tangents of the angles.

Answer 1

The Correct Option is B

Step 1: Use the known identity.
For a triangle, there is a standard identity involving the tangents of the angles: \[ \tan 2A + \tan 2B + \tan 2C = \tan 2A \tan 2B \tan 2C \]
Step 2: Conclusion.
Thus, the correct answer is \( \tan 2A \tan 2B \tan 2C \).