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?

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) (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) = 

tan(x-y) =  =  =  =  =  =   =  = 

 =  =  =  =  = 

Since it seems strange that both tan(y) and tan(x-y) can both be .  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

RELATED QUESTIONS
y=tan(x-~/4) (answered by sofiyac)

If tan(x) + tan(y) = 4 and cot(x) + cot(y) = 5, find the value of... (answered by Alan3354)

I hope you can help me :) problem is.. Find (a) tan(x+y) (b) tan(x-y) through tan x = (answered by stanbon)

Let tan cot y=4. What is tan... (answered by tommyt3rd)

sin (x + y)/ sin (x - y) = tan(x) + tan(y) / 1 + tan(x)tan(y) (answered by Alan3354)

Use the sine and cosine addition formul� to show that, for suitable x and y,... (answered by Edwin McCravy)

let x and y are acute angles, tan(x). tan(y) =1, tan(x) - tan(y) = 2 × sqrt(3)... (answered by ikleyn)

graph Y= 2 tan... (answered by jim_thompson5910)

If tan (A+B)= x and tan B =1/2 prove that tan A=2x-1/x+2 and obtain an expression in... (answered by KMST,ikleyn)