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etomac
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#1
Report Thread starter 14 years ago
#1
1, how to integrate 1/((x^2)-1)

2, prove cosine rule using vectors
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Aitch
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#2
Report 14 years ago
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(Original post by etomac)
1, how to integrate 1/((x^2)-1)

2, prove cosine rule using vectors

1 partial fractions give 0.5/(x-1) -0.5/(x+1)
(I think)

Aitch

I'll try to remember the vector one...
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RichE
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#3
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(Original post by etomac)
1, how to integrate 1/((x^2)-1)

2, prove cosine rule using vectors
For 1) use partial fractions first.

For the second, with a triangle with vertices A,B,C, we have:

a^2 = |BC|^2

= |BA + AC|^2

= |BA|^2 + |AC|^2 + 2 BA . AC

= |BA|^2 + |AC|^2 - 2 AB . AC

= c^2 + b^2 - 2 c b cos A

where . denotes the dot or scalar product, and I've used the identity

|u+v|^2 = (u+v).(u+v) = u.u + v.v + 2u.v

= |u|^2 + |v|^2 + 2u.v
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