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In any DeltaABC, prove that : (a^2 sin (...

In any `DeltaABC`, prove that : `(a^2 sin (B-C))/(sin B + sin C) + (b^2 sin (C-A))/(sin C + sin A) + (c^2 sin (A-B))/(sin A + sin B) = 0`

A

0

B

1

C

`-1`

D

2

Text Solution

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The correct Answer is:
A
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MARVEL PUBLICATION-TRIGONOMETRIC FUNCTIONS-MULTIPLE CHOICE QUESTIONS - PART - A : BUILDING-UP THE BASE (B) Properties of triangles
  1. If cos A = (sin B)/(2 sin C) , then Delta ABC is

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  2. If, in a /\ ABC, (2 cos A)/a + (cos B)/(b) + (2 cos C)/(c) = a/(bc) ...

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  3. In Delta ABC (b-c) cdot sin A + (c - a) cdot sin B + (a - b) cdot si...

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  4. In any triangle A B C , prove that following: \ (cos^2B-cos^2C)/(b+c)+...

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  5. If the sides of a triangle are x, y and sqrt((x^(2) + xy + y^(2))), t...

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  6. In any DeltaABC, prove that : (a^2 sin (B-C))/(sin B + sin C) + (b^2 s...

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  7. In any DeltaABC, prove that : (b+c) cos A + (c+a) cos B + (a+b) cos C ...

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  8. If theta is real , then: c cdot cos(A - theta) + a cdot cos(C + theta)...

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  9. In Delta ABC, (cot B + cot C)/(cot C + cot A) = ....

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  10. If : 2 sin B cdot cos C = sin A, then Delta ABC is

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  11. If A = 3B and a = 2b, then :m /B = ...

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  12. If mangleA = 60^(@), then (a+b+c)(-a+b+c)=….

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  13. If a ,c , b are in A.P., then : a cos B - b cos A = ........

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  14. In Delta ABC,(cos 2A)/(a^2) - (cos2B)/(b^2) = ......

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  15. In Delta ABC, (tan B)/(tan C) = .........

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  16. In a triangleABC, a^(2) sin 2C+c^(2) sin 2A=

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  17. If Delta ABC is right -angled at C, then: (a^2 + b^2)/(a^2 - b^2) cd...

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  18. If the angles A,B,C of Delta ABC are in A.P. And its sides a,b,c are i...

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  19. If p1,p2,p3 are the lengths of the altitudes ofa tringle from the ver...

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  20. If a^(2), b^(2), c^(2) are in A.P., then : (cos A)/a, (cos B)/b, (co...

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