Question

Evaluate $\sin {60}^{\circ }\cos {30}^{\circ }+\cos {60}^{\circ }\sin {30}^{\circ }$.

Answer 1

We know that,
$\sin {60}^{\circ }=\sqrt{3/2}=\cos {30}^{\circ }$
and $\sin {30}^{\circ }=1/2=\cos {60}^{\circ }$
Now,
$\sin {60}^{\circ }\cos {30}^{\circ }+\cos {60}^{\circ }\sin {30}^{\circ }=\left(\sqrt{3/2}\right)\left(\sqrt{3/2}\right)+\left(1/2\right)\left(1/2\right)$
$=\left(3/4\right)+\left(1/4\right)$
$=4/4$
$=1$.