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

Given:

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

To do:

We have to evaluate the given expression.

Solution:

We know that,

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

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

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

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

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

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

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

$=\frac{4}{4}$

$=1$.

$sin 60^o cos 30^o+sin 30^o cos 60^o=1$.

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Updated on: 10-Oct-2022

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