# Thread: Finding the Exact value of a tangent using sum and difference

1. ## Finding the Exact value of a tangent using sum and difference

I was wondering if someone could check if what i have so far is correct:

Tan(a - B) =

tan - 5/12 + tan 7(square root)/3
-----------------------------------------
1 - tan -(5/12) (7(square root)/3)

-5+4 7(square root)
------------------------
12
-------------------------
36 + 5 7(square root)
--------------------------
36

Flipping the bottom would get me:

-5 + 4 7 (squared) (36 - 5 7 (squared))
----------------------- ------------------------
36 + 5 7 (square) (36 - 5 7 (squared))

I'm not sure if this is correct or not, from looking at my notes the denominator
is suppose to be a number.

-180 + 25 7 (squared) + 144 7 (squared) - 20 7 (squared)
----------------------------------------------------------------------
1296 - 180 7 (squared) + 180 7 (squared) - 25 7 (squared)

2. Originally Posted by MajorJohnson
I was wondering if someone could check if what i have so far is correct:

Tan(a - B) =

tan - 5/12 + tan 7(square root)/3
-----------------------------------------
1 - tan -(5/12) (7(square root)/3)

-5+4 7(square root)
------------------------
12
-------------------------
36 + 5 7(square root)
--------------------------
36

Flipping the bottom would get me:

-5 + 4 7 (squared) (36 - 5 7 (squared))
----------------------- ------------------------
36 + 5 7 (square) (36 - 5 7 (squared))

I'm not sure if this is correct or not, from looking at my notes the denominator
is suppose to be a number.

-180 + 25 7 (squared) + 144 7 (squared) - 20 7 (squared)
----------------------------------------------------------------------
1296 - 180 7 (squared) + 180 7 (squared) - 25 7 (squared)
This looks somewhat garbled. I'm assuming that tan(A) = –5/12 and tan(B) = √7/3. The formula for tan(A–B) is (tan(A) – tan(B))/(1 + tan(A)tan(B)). So the fraction should be
....–5/12 – √7/3.... .
1 + (–5/12)(√7/3)

Multiply top and bottom by 36, to get
–15 – 12√7 .
..36 – 5√7

Next, multiply top and bottom by 36 + 5√7, so that the denominator becomes an integer.