Question

If $\cos A-\sin A=0$, then the value of cosec A is :

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $2$
• D. $3$

Answer 1

The correct option is A $\sqrt{2}$

Given, $\cos A-\sin A=0$
$\Rightarrow \cos A=\sin A$
$\Rightarrow \frac{\cos A}{\sin A}=1$

$\Rightarrow \cot A=\frac{1}{1}=\frac{b}{p}$
$h=\sqrt{b^2+p^2}=\sqrt{{\left(1\right)}^2+{\left(1\right)}^2}=\sqrt{2}$
$\therefore cosecA=\frac{h}{p}=\frac{\sqrt{2}}{1}=\sqrt{2}$