Question

How do I evaluate tan(17pi/12) using the sum identity of tangent?

Answer 1

17pi / 12 = 2pi / 3 + 3pi / 4

Answer 2

I have that part already I just don't know how to apply that to the sum identity

Answer 3

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

Answer 4

In your question, a = 2pi / 3 and b = 3pi / 4

Answer 5

would it be \[(\tan(\frac{ 2\pi}{ 3 })+\tan(\frac{ 3\pi }{ 4 })/(1-(\tan(\frac{ 2\pi}{ 3 })\tan(\frac{ 3\pi }{ 4 })\]

Answer 6

Yes

Answer 7

so would I solve that by calculator and that would be my answer?

Answer 8

Solve it part by part

Answer 9

tan (2pi / 3) = - sqrt 3
tan (3pi / 4) = -1

Answer 10

Substitute those values and simplify your fraction

Answer 11

okay thank you! :)