Question

Find the value of the following :
$\cos {45}^o\cos {60}^o-\sin {45}^o\sin {60}^o$

Answer 1

$\cos {45}^o\cos {60}^o-\sin {45}^o\sin {60}^o$
$=\frac{1}{\sqrt{2}}\times \frac{1}{2}-\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}$
$=\frac{1}{2\sqrt{2}}-\frac{\sqrt{3}}{2\sqrt{2}}=\frac{1-\sqrt{3}}{2\sqrt{2}}$