Find the exact value of tan 15degrees?

Question

Find the exact value of tan 15degrees and show work.

Answer 1

tan2A = 2tanA/(1 - tan² A)

tan30 = 2tan15/(1 - tan² 15)

1/√3 = 2tan15/ (1 - tan² 15)

1- tan² 15 = 2√3tan15

tan² 15 + 2√3tan15 - 1 = 0

tan15 = [-2√3 ± √(12 + 4)] / 2

.......... = [-2√3 ± √(16)] / 2

.......... = [-2√3 ± 4]/2

......... = -√3 + 2 ignoring negative value

Answer 2

Don't pay any attention to the first answerer.

Somewhere there is a double angle formula for Tangent. Since Tan 30 = sqrt(3)/2, you should be able to find Tan 15. Remember that an EXACT answer need not be a RATIONAL answer.