SOLUTION: What is the exact value of tan ((67 1/2)degrees) using half angle?

Question 461749: What is the exact value of tan ((67 1/2)degrees) using half angle?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
What is the exact value of tan ((67 1/2)degrees) using half angle?
..
Half angle formula for tan:
tan x/2=sin x/(1+cos x)
For given problem:
67.5=135/2=sin 135/(1+cos 135)
=sin45/(1-cos 45) (Reference angle 45� in quadrant II where sine is positive, cosine negative.)
=(√2/2)/(1-√2/2)
=√2/(2-√2) (ans)
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