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.