# Use the law of sines to deduce the law of tangent

• Dec 12th 2012, 05:58 AM
thisprecalciskillingme
Use the law of sines to deduce the law of tangent
Use the law of sines to deduce the law of tangents for triangle ABC: (a-b)/(a-b) = (tan(1/2)(A-B))/(tan(1/2)(A-B))

I've put a lot of thought into this homework problem and I hardly even know where to begin. I've attended every class and done all of the homework and none of this seems familiar to me. Any help would be much appreciated. Thanks.

a. Suppose that a, b, x, and y are real numbers such that (a/b)=(x/y), verify that (a-b)/(a+b) = (x-y)/(x+y)
b. Use the law of sines and the result in part a to show that (a-b)/(a+b)=(sinA-SinB)/((sinA+sinB)
c. Use the result in part a and the sum to product formulas to complete the derivation.
• Dec 16th 2012, 11:52 AM
StefanTM
Re: Use the law of sines to deduce the law of tangent
Hi,
we use de notations ABC with alpha, betha, gamma, a,b,c
From Sinus Formula we have:
sin(alpha)/a=sin(betha)/b => b=a*sin(betha)/sin(alpha)
=>
(a+b)/(a-b)=[(a+a*sin(betha)/sin(alpha)] / )=[(a-a*sin(betha)/sin(alpha)] =
(sin(alpha)+sin(betha))/(sin(alpha)-sin(betha))
for begin.
• Dec 21st 2012, 10:13 PM
ibdutt
Re: Use the law of sines to deduce the law of tangent
• Dec 22nd 2012, 10:49 PM
StefanTM
Re: Use the law of sines to deduce the law of tangent
Yes,
it's correct.
k =2R, where R is the radius of the triangle the content the points A,B und C of the triangle(ABC is in the circle inscreibed triangle),
see sinus formulas.