I need to evaluate tan(7pi/8) but i don't know how to split it up so that i can work with it?

Question

I need to evaluate tan(7pi/8) but i don't know how to split it up so that i can work with it?

Answer 1

tan(pi-x)=-tan(x), so

tan(7pi/8) = -tan(pi/8)

= 1-sqrt(2) !

tan(pi/4) = sin(pi/4)/cos(pi/4) = 1

We know

tan(2x) = 2tan(x)/(1-tan²(x))

1 = 2 y / (1-y²)

=> y=tan(x)=tan(pi/8)=sqrt(2)-1

(solving the quadratic equation)