Use the half-angle formulas to find the exact value of the trigonometric function?

Question

tan 7π/8

Answer 1

The half-angle formula for tangent is:

tan(½θ) = [1 - cos θ] / sin θ 

 

tan(7π/8)

= tan[ ½ (7π/4)]

= [1 - cos(7π/4)] / sin(7π/4) 

 

cos(7π/4) = √2/2

sin(7π/4) = -√2/2