How do you use the half angle identity to find cos 105?

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Answer 1 · 2014-11-06T16:38:06

Half Angle Formula

#cos(\theta/2)=pm sqrt{{1+cos theta}/2}#

First, since #105^circ# is the 2nd quadrant, cosine is negative, so by the half angle formula above,

#cos(105^circ)=cos({210^circ}/2)=-sqrt{{1+cos(210^circ)}/2}#

by #cos(210^circ)=-sqrt{3}/2#,

#=-sqrt{{1-sqrt{3}/2}/2}=-sqrt{{2-sqrt{3}}/4}=-{sqrt{2-sqrt{3}]}/2#

I hope that this was helpful.