Question
Evaluate the following:
$\cos45^\circ\cos30^\circ+\sin45^\circ\sin30^\circ$
$\cos45^\circ\cos30^\circ+\sin45^\circ\sin30^\circ$
✓
Answer
On substituting the values of varios T-ratios, we get:
$\cos45^\circ\cos30^\circ+\sin45^\circ\sin30^\circ$
$=\Big(\frac{1}{\sqrt{2}}\times\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{3}}\times\frac12\Big)$
$=\Big(\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}\Big)=\Big(\frac{\sqrt{3}+1}{2\sqrt{2}}\Big)$
$\cos45^\circ\cos30^\circ+\sin45^\circ\sin30^\circ$
$=\Big(\frac{1}{\sqrt{2}}\times\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{3}}\times\frac12\Big)$
$=\Big(\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}\Big)=\Big(\frac{\sqrt{3}+1}{2\sqrt{2}}\Big)$
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