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In triangle ABC, prove that (b/c+c/b) co...

In triangle ABC, prove that `(b/c+c/b) cosA +(a/b+b/a) cos C+(a/c+c/a)cosB=3`

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By projection formula
a=bcosC + c cos B
b=acosC + c cosA
c=a cosB + b cosA
LHS `=(b/a+c/b)cosA + (a/b+b/a) cos C+ (a/c+c/a) cosB`
`=(b/c cosA + a/c cosB) + (c/b cosA +a/b cosC) + (b/a cos C + c/a cos B)`
`=c/c+b/b + a/a`
=3
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