Question

Find the trigonometric ratios equivalent to $\mathrm{cosec}45°$

Answer 1

Find the required trigonometric ratio.

As $\mathrm{cosec\theta }=\frac{1}{\mathrm{sin\theta }}$

So, $\mathrm{cosec}\left(45°\right)=\frac{1}{\sin \left(45°\right)}$

$\Rightarrow$ $\mathrm{cosec}\left(45°\right)=\frac{1}{{\displaystyle \frac{1}{\sqrt{2}}}}\left[\because \sin \left(45°\right)=\frac{1}{\sqrt{2}}\right]$

$\Rightarrow$ $\mathrm{cosec}\left(45°\right)=\sqrt{2}$

Hence, the required trigonometric ratio is $\sqrt{2}$.