Question

How do you find the exact values of tan3pi/8 using the half angle formula?

Answer 1

Find `tan ((3pi)/8)`

Ans: `1 + sqrt2`

Explanation:

Cal `tan (3pi/8) = t`
`tan ((6pi)/8) = tan ((3pi)/4) = - 1`

Use trig identity: tan ((3pi)/4) =`-1 = (2t)/(1 - t^2)`

t^2 - 2t - 1 = 0
D = d^2 = 4 + 4 = 8 --> `d = +- 2sqrt2`

`t = tan ((3pi)/8) = 1 +- sqrt2`
Since `(3pi)/8` is in Quadrant I, only the positive answer is accepted.
`tan ((3pi)/8) = 1 + sqrt2`