SOLUTION: What is the exact value of cos(1/2*tan^-1(-5))?

Question 387971: What is the exact value of cos(1/2*tan^-1(-5))?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let . We have to find . Then , or . From the identity , we get , or .
Secant of is positive because means is in the 2nd quadrant.
Hence , or
. (Again using another identity, the double -angle identity for cosine.)
,
or . Cosine of is positive because is in quadrant 2, so when it is divided by 2, alpha must be in quadrant 1.

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