Question

If $\tan 2A=\cot (A-{18}^0)$, where 2A is an acute angle, find the value of A.

Answer 1

$\tan 2A=\cot (A-{18}^{\circ })$

$⟹\cot ({90}^{\circ }-2A)=\cot (A-{18}^{\circ })$

${90}^{\circ }-2A=A-{18}^{\circ }⟹3A={108}^{\circ }⟹A={36}^{\circ }$