Evaluate each of the following:$ \sin 60^{\circ} \cos 30^{\circ}+\cos 60^{\circ} \sin 30^{\circ} $

Given:

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

To do:

We have to evaluate \( \sin 60^{\circ} \cos 30^{\circ}+\cos 60^{\circ} \sin 30^{\circ} \).

Solution:  

We know that,

$\sin 60^{\circ}=\frac{\sqrt3}{2}$

$\sin 30^{\circ}=\frac{1}{2}$

$\cos 60^{\circ}=\frac{1}{2}$

$\cos 30^{\circ}=\frac{\sqrt3}{2}$

$ \sin 60^{\circ} \cos 30^{\circ}+\cos 60^{\circ} \sin 30^{\circ}=\frac{\sqrt3}{2}\times\frac{\sqrt3}{2}+\frac{1}{2}\times\frac{1}{2}$

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

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

$=\frac{4}{4}$

$=1$

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

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Updated on: 10-Oct-2022

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