Discussion
If \(\tan 2A = \cot(A - 18°)\), where 2A is an acute angle, find the value of A.
Answer: C
We use the identity \(\cot \theta = \tan(90° - \theta)\).
So, \(\cot(A - 18°) = \tan(90° - (A - 18°)) = \tan(108° - A)\).
The equation becomes \(\tan 2A = \tan(108° - A)\).
This implies \(2A = 108° - A\).
3A = 108°
A = 36°.
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