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In any triangle A B C , prove that follo...

In any triangle `A B C` , prove that following: `\ \ acosA+bcosB+c\ cos C=2bsinAsinC=2csinAsinB`

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Let a, b, c be the sides of any triangle A B C. Then by applying the sine rule, we get

`frac{a}{sin A}-frac{b}{sin B}-frac{c}{sin C}-k `

` a=k sin A, b=k sin B, C=k sin C`

So the LHS of the given equation, we get

`{LHS}=a cos {A}+{b} cos {B}+c cos C`

...
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