Question

In right angle $△ABC,\angle B={90}^o,\angle A={45}^o=\angle C$, then $cosec{45}^o=$

• A. $1$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. None of above

Answer 1

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

$\angle A=\angle C\Rightarrow AB=BC=a$

$AC=\sqrt{{AB}^2+{BC}^2}=\sqrt{a^2+a^2}=\sqrt{2a^2}=\sqrt{2}a$

$\csc {45}^o=\frac{hypotenuse}{base}=\frac{AC}{AB}=\frac{\sqrt{2}a}{a}=\sqrt{2}$

So, $\sqrt{2}$ is correct.