Question

Find the value of the following:
$\sin {60}^o\cos {30}^o+\cos {60}^o\sin {30}^o$

Answer 1

We know that the values of the trignometric functions $\sin {60}^0=\frac{\sqrt{3}}{2}$, $\cos {30}^0=\frac{\sqrt{3}}{2}$, $\sin {30}^0=\frac{1}{2}$ and $\cos {60}^0=\frac{1}{2}$, therefore, the value of $\sin {60}^0\cos {30}^0+\cos {60}^0\sin {30}^0$ is:

$\sin {60}^0\cos {30}^0+\cos {60}^0\sin {30}^0=(\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2})+(\frac{1}{2}\times \frac{1}{2})=\frac{3}{4}+\frac{1}{4}=\frac{4}{4}=1$

Hence, $\sin {60}^0\cos {30}^0+\cos {60}^0\sin {30}^0=1$.