tan pi/12 (find value)

Answer 1

tan π/12 = tan ((4π-3π)/12) =tan( 4π/12 - 3π/12)= tan( π/3- π/4)

The formula for tangent subtraction is

tan(a-b) = ( tan⁡(a)-tan⁡(b))/(1+tan⁡(a)tan⁡(b))

Let a= π/3 and b = π/4

tan(π/3 -π/4) = ( tan⁡(π/3 )-tan⁡(π/4))/(1+tan⁡(π/3 )tan⁡(π/4))

=(√3-1)/(1+ √3)

Now multiply top and bottom by the conjugate of the bottom

(√3-1)/(1+ √3) x (1- √3)/(1- √3) =(2√3-4)/(-2) = (2(√3-2))/(-2) = -(√3-2)