Evaluate the following: Verify the following: 60^ 30^ + 60^ 30^ =… - Vidyadip

Question

Evaluate the following:
Verify the following:
$\cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ=\cos30^\circ$

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Answer

$\cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ$
$=\Big(\frac12\Big)\times\Big(\frac{\sqrt{3}}{2}\Big)+\Big(\frac{\sqrt{3}}{2}\Big)\times\Big(\frac12\Big)$
$=\frac{\sqrt{3}}{4}+\frac{\sqrt{3}}{4}=\frac{\sqrt{3}}{2}$
Also, $\cos30^\circ=\frac{\sqrt{3}}{2}$
$\therefore\ \cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ=\cos30^\circ$

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