SOLUTION: Find the exact value of cos(2arctan(-2)).

Question 746615: Find the exact value of cos(2arctan(-2)).

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact value of cos(2arctan(-2)).
tan(x)=-2(in Q2)
opposite side=2
adjacent side=-1
hypotenuse=√(2^2+1)=√5
sin(x)=2/√5
cos(x)=-1/√5
cos(2x)=cos^2(x)-sin^2(x)=1/5-4/5=-3/5
cos(2arctan(-2))=cos(2x)=-3/5
..
Check: (with calculator)
tan(x)=-2
x≈116.5650�
2x≈233.1301(in Q3 where cos<0)
cos(2x)=-0.6000
Exact ans.=-3/5=-0.6000
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