Question

If $tan4\theta =cot(\theta -{10}^{\circ })$, where $4\theta$ and$(\theta -{10}^{\circ })$ are acute angles then the value of $\theta$ in degrees is ___.

Answer 1

$tan4\theta =cot(\theta -{10}^{\circ })$

$\Rightarrow tan4\theta =tan[{90}^{\circ }-(\theta -{10}^{\circ }\left)\right]$

$\Rightarrow$ $4\theta$ = ${90}^{\circ }-\theta +{10}^{\circ }$

$\Rightarrow$ $\theta =\frac{{100}^{\circ }}{5}$

$\Rightarrow$ $\theta$ = ${20}^{\circ }$