Question

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

Answer 1

Given $tan2A=cot(A-{18}^0)$

$\Rightarrow cot(90-2A)=cot(A-{18}^0)[\because tan\theta =cot(90-\theta \left)\right]$

Comparing angles we get

$90-2A=A-18$

$\Rightarrow 90+18=A+2A$

$\Rightarrow 3A=108$

$\Rightarrow A=\frac{108}{3}$

$\Rightarrow A={36}^{\circ }$