Question

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

• A. \( 72^\circ \)
• B. \( 36^\circ \)
• C. \( 60^\circ \)
• D. \( 45^\circ \)

Hint:

Use the identity: \[ \tan x = \cot (90^\circ - x) \] to simplify trigonometric equations.

Answer 1

The Correct Option is B

We use the identity:
\[ \tan x = \cot (90^\circ - x). \] So, equating:
\[ \tan 2A = \tan (90^\circ - (A - 18^\circ)). \] \[ 2A = 90^\circ - A + 18^\circ. \] \[ 3A = 108^\circ. \] \[ A = 36^\circ. \]