Question

Evaluate each of the following

cos${60}^{\circ }$ cos${45}^{\circ }$ - sin ${60}^{\circ }$ sin ${45}^{\circ }$

Answer 1

cos${60}^{\circ }$ = $\frac{1}{2}$

cos${45}^{\circ }$ = $\frac{1}{\sqrt{2}}$

sin ${60}^{\circ }$ = $\frac{\sqrt{3}}{2}$

sin ${45}^{\circ }$ = $\frac{1}{\sqrt{2}}$

Now,

cos${60}^{\circ }$ cos${45}^{\circ }$ - sin ${60}^{\circ }$ sin ${45}^{\circ }$

= $\frac{1}{2}$ $\times$ $\frac{1}{\sqrt{2}}$ - $\frac{\sqrt{3}}{2}$$\times$ $\frac{1}{\sqrt{2}}$

= $\frac{1}{2\sqrt{2}}$ - $\frac{\sqrt{3}}{2\sqrt{2}}$

= $\frac{1-\sqrt{3}}{2\sqrt{2}}$