Question

use half-angle identities to find the exact value of tan 3pi/8

Answer 1

does it help to know that \(\frac{3\pi}{8}\) is half of \(\frac{3\pi}{4}\) ?

Answer 2

i rather have it solved, please, this one too, tanx(sinx+cotxcosx)=secx

Answer 3

Call t = tan a/2 = tan 3Pi/8. Use trig identity: tan a = 2t/(1 - t^2).
tan 3Pi/4 = 2t/(1 - t^2) = -1 (trig table gives tan 3Pi/4 = -1)
2t = -(1 - t^2) = -1 + t^2 --> t^2 - 2t - 1 = 0.
Use the formula to solve this quadratic equation. It has 2 real roots:
x1 = 1 + V2 and x2 = 1 - V2.
Since tan 3Pi/8 is positive (tan 3Pi/4 < 0), then x2 is rejected.