Question

Evaluate each of the following

sin ${45}^o$ sin ${30}^o$ + cos ${45}^o$ cos ${30}^o$

Answer 1

sin ${45}^o$ sin ${30}^o$ + cos ${45}^o$ cos ${30}^o$

=( $\frac{1}{\sqrt{2}}$)( $\frac{1}{2}$) + ( $\frac{1}{\sqrt{2}}$)( $\frac{\sqrt{3}}{2}$)

=( $\frac{1}{\sqrt{2}}$)( $\frac{1}{2}$) + ( $\frac{1}{\sqrt{2}}$)( $\frac{\sqrt{3}}{2}$)
= $\frac{1}{2\sqrt{2}}$ + $\frac{3}{2\sqrt{2}}$
= $\frac{4}{2\sqrt{2}}$
= $\frac{2}{\sqrt{2}}$
= $\frac{\sqrt{2}\times \sqrt{2}}{\sqrt{2}}$
= $\sqrt{2}$