How do you use a half-angle formula to simplify $cos(-337.5)$ ?

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Answer 1 · 2015-05-23T14:38:47

Use the trig identity: 2cos^2 x = 1 - cos 2x

$2cos(-337.5)^2 = 1 - cos (675)$

On the trig unit circle,
$cos (675) = cos (-45 + 2(360)) = cos 45 = sqrt2/2$

$cos^2 (-375) = 1 - (sqrt2)/2 = (2 - sqrt2)/4$

How do you use a half-angle formula to simplify cos(-337.5)cos(-337.5)?