Help with Trigonometry Please? Sum and Addition of Tangent!?

Question

K so the question reads: Tan (2 pie over 3 + pie over 4) I'm so confused as to what to do next. I've got the formula to plug it into but I'm confused as to whether or not I figure out the Tangent of 1 pie over 3 and then plug it in, or just plug in 2 pie over three itself. Help por favor?

Answer 1

tan(A+B)=tanA+tanB / (1-tanAtanB)
tan(2pi/3+pi/4)
=(tan2pi/3+tanpi/4)/(1-tan2pi/3tanpi/4)
=-rt3+1/1+rt3
rationalising
(rt3-1)(1-rt3)/(3-1)
-4-2rt3/2=-(2+rt3)

Answer 2

You have tan ((2pi/3)+(pi/4)

Then using the formula, you get

tan(2pi/3) + tan(pi/4)
----------------------------
1 - tan(2pi/3) tan(pi/4)

Did you get this far?

If so, you just figure out that:
tan(2pi/3) = -sqrt(3)
tan(pi/4) = 1

Substitute those answers to the trig functions and rest is plain algebra.

As to if you use pi/3 or 2pi/3, think of this as angles in the unit circle. pi/3 will put you in the second quadrant and 2pi/3 in the third. The value happens to be sqrt(3) and -sqrt(3), but that really doesn't matter. You put the angle which is 2pi/3 for the argument to the tangent.