Evaluate each of the following

Question:

Evaluate each of the following

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

Solution:

We have to find the value of the expression

$\sin 60^{\circ} \cos 30^{\circ}+\cos 60^{\circ} \sin 30^{\circ}$....(1)

Now $\sin 60^{\circ}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}, \sin 30^{\circ}=\cos 60^{\circ}=\frac{1}{2}$

So by substituting above values in equation (1)

We get,

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

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

$=\frac{3}{4}+\frac{1}{4}$

$=\frac{3+1}{4}$

$=\frac{4}{4}$

$=1$

Therefore,

$\sin 60^{\circ} \cos 30^{\circ}+\cos 60^{\circ} \sin 30^{\circ}=1$