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In a DeltaABC,((b)/(c)+(c)/(b))cosA+((a)...

In a `DeltaABC,((b)/(c)+(c)/(b))cosA+((a)/(b)+(b)/(a))cosC+((a)/(c)+(c)/(a))cosB` is equal to

A

4

B

5

C

3

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Using projection formulae, `a=bcosC+c CosB`
`b=acosC+c cosA`
`c=acosB+bcosA`
Given that ,
`((b)/(c)+(c)/(b))cosA+((a)/(b)+(b)/(a))cosC+((a)/(c)+(c)/(a))cosB`
`=((b)/(c)"cos"A+(a)/(c)"cos"B)+((c)/(b)"cos"A+(a)/(b)"cos"C)+((b)/(a)"cos"C+(c)/(a)"cos"B)`
`=(c)/(c)+(b)/(b)+(a)/(a)=3`
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