Question

In a right angled triangle ABC, right angled at C, if $\tan A=\cot B$, then what is value of A + B?

Answer 1

Given that, $\tan A=\cot B$
We know that,
$\tan A=\cot ({90}^{\circ }-A)$
Subsituting the value of $\tan A$ into $\tan A=\cot B$.
$\cot ({90}^{\circ }-A)=\cot B$
So, ${90}^{\circ }$ - A = B
A + B = ${90}^{\circ }$