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Algebra

Blazing goIITian

 Joined: 14 May 2007 Post: 822
20 May 2007 19:35:21 IST
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solution of triangles(easy one)
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

If in a triangle, angleC = 60 degraees, then prove that
1/(a+c) + 1/(b+c) = 3/(a+b+c)

Hot goIITian

Joined: 26 Jan 2007
Posts: 156
20 May 2007 19:48:48 IST
1 people liked this

Given,
angle C =pi/3

We have to prove,
1/(a+c) + 1/(b+c) = 3/(a+b+c)     (ie)

1 +  b/(a+c)  + 1 + a/(b+c) =3     (ie)

b2 + bc = (a+c)(b+c-a)               (ie)

a2 + b2 -c2 = ab                         (ie)

(
a2 + b2 -c2 )/2ab = 1/2  = cos(pi/3)  which is cosine formula for angle C.

therefore proved.

That soles the problem!

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