Question

If $\tan A=\cot B,$ prove that $A+B={90}^{\circ }.$

Answer 1

$\tan A=\cot B$

$\Rightarrow \cot \theta =\tan (90-\theta )$

$\Rightarrow \tan A=\tan (90-B)$

$\Rightarrow A=90-B$

$\Rightarrow A+B=90°$

Hence, proved.