Question
Evaluate the following:
$\cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ$
$\cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ$
✓
Answer
On substituting the values of varios T-ratios, we get:
$\cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ$
$=\Big(\frac{1}{2}\times\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2}\times\frac12\Big)$
$=\Big(\frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}\Big)=0$
$\cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ$
$=\Big(\frac{1}{2}\times\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2}\times\frac12\Big)$
$=\Big(\frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}\Big)=0$
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