Question

Find the value of tan(pi/8).

Answer 1

Since π8π8 is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.π8π8 is not an exact angleFirst, rewrite the angle as the product of 1212 and an angle where the values of the six trigonometric functions are known. In this case, π8π8 can be rewritten as (12)⋅π412⋅π4.tan((12)⋅π4)tan12⋅π4Use the half-angle identity for tangent to simplify the expression. The formula states that tan(θ2)=sin(θ)1+cos(θ)t⁢a⁢n⁢θ2=sinθ1+cosθ.sin(π4)1+cos(π4)sinπ41+cosπ4Simplify the result.
√2−1