Question

Evaluate the expression: \[ \tan 6^\circ \tan 42^\circ \tan 66^\circ \tan 78^\circ \]

• A. \( \frac{3}{4} \)
• B. \( 1 \)
• C. \( 0 \)
• D. \( \frac{1}{3} \)

Hint:

The product of complementary tangent functions \( \tan A \tan (90^\circ - A) \) simplifies to 1.

Answer 1

The Correct Option is B

Using the identity: \[ \tan A \tan (90^\circ - A) = 1 \] we pair the terms: \[ \tan 6^\circ \tan 84^\circ, \quad \tan 42^\circ \tan 48^\circ \] Since: \[ \tan 6^\circ \tan 84^\circ = 1, \quad \tan 42^\circ \tan 48^\circ = 1 \] Multiplying both results: \[ 1 \times 1 = 1 \] Thus, the correct answer is \( 1 \).