Question

If $tan2\theta =cot(\theta +6^{\circ })$ where $2\theta$ and $(\theta +6^{\circ })$ are acute angles, find the value of $\theta$.

Answer 1

$tan2\theta =cot(\theta +6^{\circ })$

$\Rightarrow cot({90}^{\circ }-2\theta )=cot(\theta +6^{\circ })$

$\Rightarrow {90}^{\circ }-2\theta =\theta +6^{\circ }\Rightarrow 3\theta ={84}^{\circ }\Rightarrow \theta ={28}^{\circ }$