Question

the exact value of tan 5pi/12 is?

Answer 1

This will use the half-angle formula which is: tan(ø/2) = (1 - cosø)/sinø

If ø/2 = -5π/12, ø = -5π/6.

So, -tan(-5π/12) = -(1 - cos(-5π/6))/sin(-5π/6). Now simplify:
-tan(-5π/12) = (cos(-5π/6) - 1)/sin(-5π/6). Distributing the -1 in.
cos(-5π/6) = -(√3)/2 and sin(-5π/6) = -1/2. Substituting we get:
-tan(-5π/12) = (-(√3)/2 - 1)/(-1/2).
-tan(-5π/12) = ((√3)/2 + 1)/(1/2). Negatives cancel.
-tan(-5π/12) = (√3) + 2. Multiply by 2 to remove the denominator.
So there's your answer: (√3) + 2.

Answer 2

Hope that helps

Answer 3

thank you!! it did help a lot

Answer 4

would 2+sqrt3 work too?

Answer 5

@darkb0nebeauty