Question

if tan beta is equal to COT beta then find the value of alpha + beta​

Answer 1

$\textbf{Given:}$

$tan\alpha=cot\beta$

$\text{We know that}$

$\bf\,cot\,\theta=tan(90^{\circ}-\theta)$

$\implies\,tan\alpha=tan(90^{\circ}-\beta)$

$\implies\,\alpha=90^{\circ}-\beta$

$\implies\,\alpha+\beta=90^{\circ}$

$\therefore\boxed{\bf\alpha+\beta=90^{\circ}}$