SOLUTION: Is the exact value of tan(7pi/8)=(1-sqrt2)?

Algebra ->  Trigonometry-basics -> SOLUTION: Is the exact value of tan(7pi/8)=(1-sqrt2)?      Log On


   

Question 851541: Is the exact value of tan(7pi/8)=(1-sqrt2)?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Is the exact value of tan(7pi/8)=(1-sqrt2)?
tan%287%28pi%29%2F8%29=tan%28%287%28pi%29%2F4%29%2F2%29
Identity: tan%28x%2F2%29=sin%28x%29%2F%281%2Bcos%28x%29%29
sin%28x%29=sin%287%28pi%29%2F4%29=-sqrt%282%29%2F2 (in quadrant IV in which sin<0)
cos%28x%29=cos%287%28pi%29%2F4%29=sqrt%282%29%2F2 (in quadrant IV in which cos>0)

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