SOLUTION: I am confused on the tan(x-y) if tan x = 24/7 and tan y = -4/3...how is tan (x-y) = -4/3?

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Question 756774: I am confused on the tan(x-y) if tan x = 24/7 and tan y = -4/3...how is tan (x-y) = -4/3?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I am confused on the tan(x-y) if tan x = 24/7 and tan y = -4/3...how is tan (x-y) = -4/3?
I agree it seems strange that tan(x-y) and tan(y) are the same, but it's
a fact here.  [It has to do with the fact that both angles are from integer right triangles.  x is from a 7-24-25 right triangle and y is from a 3-4-5
right triangle.

Use the identity:

tan(x-y) = %28tan%28x%29-tan%28y%29%29%2F%281%2Btan%28x%29tan%28y%29%29

tan(x-y) = %28tan%28x%29-tan%28y%29%29%2F%281%2Btan%28x%29tan%28y%29%29 = %2824%2F7-%28-4%2F3%29%29%2F%281%2B%2824%2F7%29%28-4%2F3%29%29 = %2824%2F7%2B4%2F3%29%2F%281-%2824%2F7%29%284%2F3%29%29 = %2824%2F7%2B4%2F3%29%2F%281-%28%22%22%5E8cross%2824%29%2F7%29%284%2Fcross%283%29%29%29 = %28%2824%2A3%29%2F%287%2A3%29%2B%284%2A7%29%2F%283%2A7%29%29%2F%281-%288%2F7%29%284%29%29 =  %2872%2F21%2B28%2F21%29%2F%281-32%2F7%29 = %28100%2F21%29%2F%287%2F7-32%2F7%29 = 

%28100%2F21%29%2F%28-25%2F7%29 = %28100%2F21%29%2A%28-7%2F25%29 = -%28100%2F21%29%2A%287%2F25%29 = -%28%22%22%5E4cross%28100%29%2F21%29%2A%287%2Fcross%2825%29%29 =  = -4%2F3

Since it seems strange that both tan(y) and tan(x-y) can both be -4%2F3.  let's check it with a calculator:

x = 73.73979529°, y=126.8398976°

x-y = 73.73979529° - 126.8398976° = -53.13010235°

tan(y) = tan(126.8398976°) = -1.333333333

tan(x-y) = tan(-53.13010235) = -1.333333333

So you see that, strange as it seems, this is the case!

Edwin