# Working with half-angle identity

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Cos x (using the half-angle identity)

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddfhttps://brainmass.com/math/geometry-and-topology/working-half-angle-identity-13879

## SOLUTION This solution is **FREE** courtesy of BrainMass!

We have the half angle identity for cos x as,

cos x = +-sqrt[(1 + cos 2x)/2]

also, cos 7pi/12 = cos 105 = cos (210/2)

so, cos 105 = -sqrt[(1 + cos 210)/2]

(since 105 degrees is in quadrant II and cos is negative there)

Therefore,

cos 105 = -sqrt[(1 + cos{2*90 + 30})/2]

= -sqrt[(1 + -cos 30)/2]

= -sqrt[(1 - (sqrt3)/2)/2] (cos 30 = [sqrt3]/2)

= -sqrt[{2 - sqrt3}/4]

= -0.25881

which is the required value

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf>https://brainmass.com/math/geometry-and-topology/working-half-angle-identity-13879