Question

If \( \tan 2A = \cot(A - 18^\circ) \), where \( 2A \) is an acute angle, then the value of \( A \) is:

• A. 72°
• B. 36°
• C. 60°
• D. 45°

Hint:

For \( \tan x = \cot y \), use the identity \( \cot y = \tan(90^\circ - y) \) to relate the angles.

Answer 1

The Correct Option is B

We are given that \( \tan 2A = \cot(A - 18^\circ) \). Using the identity \( \cot x = \tan(90^\circ - x) \), we can rewrite the equation as: \[ \tan 2A = \tan(90^\circ - (A - 18^\circ)) = \tan(108^\circ - A). \] Since \( \tan x = \tan y \), we can equate the arguments: \[ 2A = 108^\circ - A. \] Solving for \( A \): \[ 3A = 108^\circ \quad \Rightarrow \quad A = 36^\circ. \] Thus, the value of \( A \) is \( \boxed{36^\circ} \).