Question

# Evaluate the following: $\sin 45^\circ \sin 30^\circ + \cos 45^\circ \cos 30^\circ$

As we know the value of$\sin 45^\circ = \cos 45^\circ = \dfrac{1}{{\sqrt 2 }}$, the value of$\sin 30^\circ = \dfrac{1}{2}$, and the value of$\cos 30^\circ = \dfrac{{\sqrt 3 }}{2}$,
$\Rightarrow \sin 45^\circ \sin 30^\circ + \cos 45^\circ \cos 30^\circ = \left( {\dfrac{1}{{\sqrt 2 }}} \right)\left( {\dfrac{1}{2}} \right) + \left( {\dfrac{1}{{\sqrt 2 }}} \right)\left( {\dfrac{{\sqrt 3 }}{2}} \right)$
$= \dfrac{1}{{2\sqrt 2 }}\left( {1 + \sqrt 3 } \right)$