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In any Delta ABC,sum a sin (B -C) =...

In any `Delta` ABC,`sum` a sin (B -C) =

A

2s

B

a+b+c

C

`a^(2)+b^(2)+c^(2)`

D

0

Text Solution

Verified by Experts

Using Sine rule `(sinA)/a=(SinB)/b=(SinC)/c`=k , we have
`suma sin (B-C)`
= `k sum sin A sin (B - C)`
`= k sum sin ( B + C) sin ( B - C)`
`= k sum (sin^(2) B-sin^(2) C)`
`= k {(sin^(2) B-sin^(2)C)+(sin^(2)C - sin^(2) A)+ (sin^(2) A -sin^(2) B)}`
`= kxx0=0`
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OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
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  11. In a DeltaABC, AD is the altitude from A. Given bgtc ,angleC=23^(@) an...

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  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

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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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  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

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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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  20. If in DeltaABC, a=2b and A=3B, then A is equal to

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  21. Let the angles A , B and C of triangle A B C be in AdotPdot and let b ...

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