Question

Given: $\angle$ A and $\angle$ B are less than ${90}^{\circ }$. If A+B = ${90}^{\circ }$, then the value of tan A $\times$ tan B is

• A. 0.0
• B. 1
• C. not defined
• D. 2

Answer 1

The correct option is B 1

Given: A+B = ${90}^{\circ }$
$\Rightarrow$ B = ${90}^{\circ }$ - A
$\because$ tan $({90}^{\circ }-\theta$) = cot $\theta$
$\therefore$ tan B = tan (${90}^{\circ }$ - A) = cot A

$\therefore$ tan A $\times$ tan B = tan A $\times$ cot A

$\because$ cot A = $\frac{1}{tanA}$

$\therefore$ tan A $\times$ tan B = 1