Question

find the value of tan pie/8???

Answer 1

tan(A+B) = (tanA + tanB) / (1 - tanAtanB) 
If A+B 
tan(2A) = 2tan(A) / (1 - tan²A) 

tan(π/4) = 2tan(π/8) / (1 - tan²(π/8)) 
1 = 2tan(π/8) / (1 - tan²(π/8)) 

tan(π/8) = x 
Note: π/8 is in the first quadrant so tan(π/8)>0. x>0 

1 = 2x/(1-x²) 
1-x² = 2x 
x² + 2x - 1 = 0 
x = [-2±sqrt(2²+4)]/2 
= [-2±2sqrt(2)]/2 
= -1±sqrt(2) 

x>0 
x = sqrt(2) - 1 

tan(π/8) = sqrt(2) - 1

Answer 2

= sqrt ( 2 ) - 1 (answer).