Evaluate:
${s i n}^{2} 45^{o} - s i n^{2} 15^{o}$

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Solution

${sin}^{2} 45^{\circ} - {sin}^{2} 15^{\circ}$
$= (sin 45^{\circ} - sin 15^{\circ}) (sin 45^{\circ} + sin 15^{\circ})$
$= 2 cos (\frac{60}{2}) sin (\frac{30}{2}) 2 sin (\frac{60}{2}) cos (\frac{30}{2})$
$= 2 sin 30^{\circ} cos 30^{\circ} \times 2 sin 15^{\circ} cos 15^{\circ}$
$= sin 60^{\circ} sin 30^{\circ}$
$= \frac{\sqrt{3}}{2} \times \frac{1}{2}$
$= \frac{\sqrt{3}}{4}$

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