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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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