Question

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

Answer 1

Apply basic trigonometric Identities

Acute angles are those angle which are less than $90°$

$\Rightarrow A$is in First Quadrant.

$$\begin{gathered} \tan \left(2\mathrm{A}\right)=\cot \left(90°-2\mathrm{A}\right)\left[\because \tan \left(\mathrm{\theta }\right)=\cot \left(90°-\mathrm{\theta }\right)\right] \\ \Rightarrow \cot \left(90°-2\mathrm{A}\right)=\cot \left(\mathrm{A}-18°\right) \\ \Rightarrow 90°-2\mathrm{A}=\mathrm{A}-18° \\ \Rightarrow \mathrm{A}=36° \end{gathered}$$

Hence Value of A is $36°$.