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In a `DeltaABC`, if the sides a, b, c are the roots of the equation `x^(3)-11x^(2)+38x-40=0`, then `(cosA)/a+(cosB)/b+(cosC)/c=`

A

`16/9`

B

`3/4`

C

`4/3`

D

`9/16`

Text Solution

Verified by Experts

We have,
a + b + c = 11, ab + bc + ca= 38 and abc = 40
`therefore(cosA)/a+(cosB)/b+(cosC)/c=(a^(2)+b^(2)+c^(2))/(2abc)`
`=((a+b+c)^(2)-2(ab+bc+ca))/(2abc)=(121-2xx38)/(2xx40)=9/16`
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OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
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  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

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  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

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  14. Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite...

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  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

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  17. In a DeltaABC, A=(2pi)/3, b-c=3sqrt3 cm and area(DeltaABC)=(9sqrt3)/2 ...

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  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

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  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

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