document.write( "Question 851541: Is the exact value of tan(7pi/8)=(1-sqrt2)? \n" ); document.write( "

Algebra.Com's Answer #512833 by lwsshak3(11628) $\"\"$ $\"About$

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Is the exact value of tan(7pi/8)=(1-sqrt2)?
\n" ); document.write( " $\"tan%287%28pi%29%2F8%29=tan%28%287%28pi%29%2F4%29%2F2%29\"$
\n" ); document.write( "Identity: $\"tan%28x%2F2%29=sin%28x%29%2F%281%2Bcos%28x%29%29\"$
\n" ); document.write( " $\"sin%28x%29=sin%287%28pi%29%2F4%29=-sqrt%282%29%2F2\"$ (in quadrant IV in which sin<0)
\n" ); document.write( " $\"cos%28x%29=cos%287%28pi%29%2F4%29=sqrt%282%29%2F2\"$ (in quadrant IV in which cos>0)
\n" ); document.write( "

\n" ); document.write( "The exact value of tan(7pi/8)= $\"-sqrt%282%29%2F%282%2Bsqrt%282%29%29\"$ ≈-0.4142
\n" ); document.write( " $\"1-sqrt%282%29\"$ ≈-0.4142
\n" ); document.write( "It appears the answer is yes. \n" ); document.write( "

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