Question

The value of tan 2°. tan 4°. tan 6°... tan 88° is

• A. 0
• B. 1
• C. 2
• D. Not defined

Answer 1

The Correct Option is B

The given expression is: \[ \tan 2^\circ \cdot \tan 4^\circ \cdot \tan 6^\circ \cdots \tan 88^\circ \] This product involves tangent values for angles from \( 2^\circ \) to \( 88^\circ \). Notice that: \[ \tan(90^\circ - \theta) = \cot(\theta) \] Thus, for each pair of terms in the product, such as \( \tan 2^\circ \) and \( \tan 88^\circ \), we have: \[ \tan 2^\circ \cdot \tan 88^\circ = 1 \] Similarly: \[ \tan 4^\circ \cdot \tan 86^\circ = 1, \quad \tan 6^\circ \cdot \tan 84^\circ = 1, \quad \dots \] This pattern continues for all pairs, leading to a total product of 1. Therefore, the value of the expression is: \[ {1} \]

The correct option is (B): \(1\)