Question

Use a sum or difference formula to find the exact value of the trig function;
tan(105*)
Please show detailed work, thank you...

Answer 1

tan105=(tan135-tan30)/(1+tan135tan30)

Answer 2

I've gotten to the point above, but I do not know how to simplify.

Answer 3

(-1-sqrt3/3)/(1+(-1)(sqrt3/3))

Answer 4

105 comes from what angles?

Answer 5

135-30

Answer 6

and 135 is also known as?

Answer 7

180-135 = 45

Answer 8

(3pi)/4

Answer 9

45 is simpler to evaluate with

Answer 10

i see you went straight for the tan(a+b) instead of wasting time with the sin(a+b)/cos(a+b)

Answer 11

i can never really recall which tan is the right one so I just go by the sin cos

sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
-------------------------------
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)



sin(30)cos(45) + sin(45)cos(30)
----------------------------
cos(30)cos(45) -sin(30)sin(45)

Answer 12

1/2 sqrt(2)/2 + sqrt(2)/2 sqrt(3)/2
------------------------------
sqrt(3)/2 sqrt(2)/2 - 1/2 sqrt(2)/2


sqrt(2)/4 + sqrt(6)/4
------------------
sqrt(6)/4 - sqrt(2)/4


sqrt(2) + sqrt(6)
-------------
sqrt(6) - sqrt(2)

seems to fit

Answer 13

do a conjugate of the bottom to see if we can simplify it more

Answer 14

(-sqrt2+sqrt6)-(sqrt6-sqrt2)

Answer 15

I do not know what a conjugate is

Answer 16

sqrt(2) + sqrt(6) sqrt(6) + sqrt(2)
------------- --------------
sqrt(6) - sqrt(2) sqrt(6) + sqrt(2)



8 + 4 sqrt(3)
-----------
6 - 2




8 + 4 sqrt(3)
-----------
4


2 + sqrt(3)

with any luck that checks out with the wolf

Answer 17

http://www.wolframalpha.com/input/?i=tan%28105%29

yep, just gotta place it in the correct quadrant for sign

Answer 18

a conjugate is a name for a pair of ..... well

(a+b) (a-b) is a conjugate pair

Answer 19

OK, thank you for your time and effort

Answer 20

youre welcome