Question
Evaluate the following:
$\sin 45^{\circ} \sin30^{\circ} +\cos 45^{\circ} \cos30^{\circ}$
$\sin 45^{\circ} \sin30^{\circ} +\cos 45^{\circ} \cos30^{\circ}$
✓
Answer
$\sin 45^{\circ} \sin30^{\circ} +\cos 45^{\circ} \cos30^{\circ}\ \dots(1)$ We know that by trigonometric ratios we have, $\sin45^\circ =\frac{1}{\sqrt2}\ \sin30^\circ=\frac{1}{\sqrt2}$ $\cos45^\circ=\frac{1}{\sqrt2}\ \cos30^\circ=\frac{\sqrt3}{2}$ Substituting the values in (i) we get $\frac{1}{\sqrt2}.\frac{1}{2}+\frac{1}{\sqrt2}.\frac{\sqrt3}{2}$$=\frac{1}{\sqrt2}.\frac{\sqrt3}{2\sqrt2}=\frac{\sqrt3+1}{2\sqrt2}$
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