SOLUTION: given ∆ABC is isosceles with angleB = angleC, show that 2cotA = tanB - cotB

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Question 1003700: given ∆ABC is isosceles with angleB = angleC, show that 2cotA = tanB - cotB
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
2cot%28A%29+=+tan%28B%29+-+cot%28B%29

We work with the left side.

given isosceles triangle ABC, with B = C we have:

A+B+C = 180°
A+B+B = 180°
A+2B = 180°
A = 180° - 2B
cot(A) = cot(180°-2B) = -cot(2B)

So the left side

2cot%28A%29  becomes

-2cot%282B%29

-2%28cos%282B%29%2Fsin%282B%29%29

-2%28%28cos%5E2%28B%29-sin%5E2%28B%29%29%2F%282sin%28B%29cos%28B%29%29%29



-%28%28cos%5E2%28B%29-sin%5E2%28B%29%29%2F%28sin%28B%29cos%28B%29%29%29

%28-cos%5E2%28B%29%2Bsin%5E2%28B%29%29%2F%28sin%28B%29cos%28B%29%29

%28-cos%5E2%28B%29%29%2F%28sin%28B%29cos%28B%29%29%22%22%2B%22%22%28sin%5E2%28B%29%29%2F%28sin%28B%29cos%28B%29%29

%28-cos%5Ecross%282%29%28B%29%29%2F%28sin%28B%29cross%28cos%28B%29%29%29%22%22%2B%22%22%28sin%5Ecross%282%29%28B%29%29%2F%28cross%28sin%28B%29%29cos%28B%29%29

-cos%28B%29%2Fsin%28B%29%2Bsin%28B%29%2Fcos%28B%29

-cot%28B%29%2Btan%28B%29

tan%28B%29-cot%28B%29

Edwin