Question

What is the value of $\cos {1485}^0\times \text{cosec}{855}^0$?

Answer 1

$\cos \left({1485}^0\right)=\cos ({360}^0\times 4+{45}^0)$
$=\cos {45}^0=\frac{1}{\sqrt{2}}$
$co\sec {855}^0=co\sec ({360}^0\times 2+{135}^0)$
$=co\sec {135}^0$
$=co\sec ({90}^0+{45}^0)=\sec {45}^0=\sqrt{2}$
$\therefore \cos {1485}^0\times co\sec {855}^0=\frac{1}{\sqrt{2}}\times \sqrt{2}=1$