Question

If $tan2A=cot(A-{18}^{\circ })$, where 2A is an acute angle, find the value of A.

Answer 1

$tan2A=cot(A-{18}^{\circ })$
$\Rightarrow cot({90}^{\circ }-2A)=cot(A-{18}^{\circ })$ (As tan A = cot (${90}^{\circ }$ - A))
Equating angles,
$\Rightarrow {90}^{\circ }-2A=A-{18}^{\circ }\Rightarrow {108}^{\circ }=3A\Rightarrow A={36}^{\circ }$