Question

If $\tan \theta =\cot (30+\theta ),$ find the value of $\theta$

Answer 1

Given $\tan \theta =\cot ({30}^{\circ }+\theta )$

$⟹\cot ({90}^{\circ }-\theta )=\cot ({30}^{\circ }+\theta )$

$⟹{90}^{\circ }-\theta ={30}^{\circ }+\theta$

$⟹2\theta ={90}^{\circ }-{30}^{\circ }$

$⟹\theta ={30}^{\circ }$