Question

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

• A. 1
• B. 0.0
• C. not defined

Answer 1

The correct option is A 1

Given: A+B = ${90}^{\circ }$

$\Rightarrow$ B = ${90}^{\circ }$ - A

$\because$ sec $({90}^{\circ }-\theta$) = cosec $\theta$

$\therefore$ sec B = sec (${90}^{\circ }$ - A) = cosec A

$\therefore$ sin A $\times$ sec B = sin A $\times$ cosec A

$\because$ cosec A = $\frac{1}{sinA}$

$\therefore$ sin A $\times$ sec B = 1