document.write( "Question 746615: Find the exact value of cos(2arctan(-2)).
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Algebra.Com's Answer #454424 by lwsshak3(11628)\"\" \"About 
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Find the exact value of cos(2arctan(-2)).
\n" ); document.write( "tan(x)=-2(in Q2)
\n" ); document.write( "opposite side=2
\n" ); document.write( "adjacent side=-1
\n" ); document.write( "hypotenuse=√(2^2+1)=√5
\n" ); document.write( "sin(x)=2/√5
\n" ); document.write( "cos(x)=-1/√5
\n" ); document.write( "cos(2x)=cos^2(x)-sin^2(x)=1/5-4/5=-3/5
\n" ); document.write( "cos(2arctan(-2))=cos(2x)=-3/5
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\n" ); document.write( "Check: (with calculator)
\n" ); document.write( "tan(x)=-2
\n" ); document.write( "x≈116.5650º
\n" ); document.write( "2x≈233.1301(in Q3 where cos<0)
\n" ); document.write( "cos(2x)=-0.6000
\n" ); document.write( "Exact ans.=-3/5=-0.6000 \n" ); document.write( "
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