Question

If $\tan 9\theta =\cot \theta$, where $9\theta <{90}^o$ then find the value of $\theta$.

Answer 1

Given $\tan 9\theta =\cot \theta$ and $9\theta <{90}^{\circ }⟹\theta <{10}^{\circ }$

$\tan 9\theta =\tan ({90}^{\circ }-\theta )$

$⟹9\theta ={90}^{\circ }-\theta$

$⟹10\theta ={90}^{\circ }$

$⟹\theta =9^{\circ }$