Without using the trigonometric tables, find
a) $sin 15^{o}$
b) $cos 15^{o}$

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Solution

$sin 15 = sin (45 - 30)$
$= sin 45 cos 30 - cos 45 sin 30$
$= \frac{\sqrt{3}}{2 \sqrt{2}} - \frac{1}{2 \sqrt{2}} = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$
$cos 15 = cos (45 - 30)$
$= cos 45 cos 30 + sin 45 sin 30$
$= \frac{\sqrt{3}}{2 \sqrt{2}} + \frac{1}{2 \sqrt{2}}$
$= \frac{\sqrt{3} + 1}{2 \sqrt{2}}$

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