How do you use the sum and difference formula to simplify $cos 15$ $cos15$ ?

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Answer 1 · 2016-10-12T17:58:49

see below

${cos 15}^{\circ} = cos (45^{\circ} - 30^{\circ})$ $cos 15^@=cos(45^@-30^@)$

$= {cos 45}^{\circ} {cos 30}^{\circ} + {sin 45}^{\circ} {sin 30}^{\circ}$ $=cos45^@cos30^@+sin45^@sin30^@$

$= \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2}$ $=sqrt2/2* sqrt3/2+sqrt2/2 *1/2$

$= \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}$ $=sqrt6/4+sqrt2/4$

$= \frac{\sqrt{6} + \sqrt{2}}{4}$ $=(sqrt6+sqrt2)/4$

How do you use the sum and difference formula to simplify cos15cos15?