What is the value of cos 75°?

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What is the value of cos 75°?

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Answer 1 · 2015-11-21T01:17:28

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

Explanation:

Apply the trig identity: cos (a + b) = cos a.cos b - sin a.sin b
$cos (75) = cos (30 + 45) = cos 30 \cdot cos 45 - sin 30 \cdot sin 45 =$ $cos (75) = cos (30 + 45) = cos 30*cos 45 - sin 30*sin 45 =$
= $(\frac{\sqrt{3}}{2}) (\frac{\sqrt{2}}{2}) - (\frac{1}{2}) (\frac{\sqrt{2}}{2}) = \frac{\sqrt{6} - \sqrt{2}}{4}$ $(sqrt3/2)(sqrt2/2) - (1/2)(sqrt2/2) = (sqrt6-sqrt2)/4$

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What is the value of cos 75°?

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