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(iv) a sin (B-C) + b sin(C-A) + c sin (A...

(iv) `a sin (B-C) + b sin(C-A) + c sin (A-B)=0`

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For any triangle ABC show that a sin(B-C)+bsin(C-A)+csin(A-B)=0

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Simplify: cosA sin(B - C) + cos B sin (C - A) + cosC sin(A -B)

Simplify: sin (B + C) sin (B - C) + sin (C + A) sin (C - A) + sin(A + B) sin (A - B)

Show that 4 sin A sin Bsin C = sin(A+B-C) + sin (B+C-A) + sin(C+A-B)-sin(A+B+C).

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(ix) (a^(2) sin (B-C))/(sinA) + (b^(2) sin (C-A))/(sin B) + (c^(2) sin (A-B))/(sin C)=0

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CHHAYA PUBLICATION-PROPERTIES OF TRIANGLE -Short Answer Type Questions
  1. (ii) (b-c) cos( A/2) = a sin ((B-C)/2)

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  2. (iii) a cosA + b cos B + c cos C = 4R sin A sin B sinC

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  3. (iv) a sin (B-C) + b sin(C-A) + c sin (A-B)=0

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  4. (v) (b^(2)-c^(2))/(cos B + cos C) + (c^(2)-a^(2))/( cos C + cosA) + (a...

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  5. (vi) a cos B cos C + b cos C cosA + c cosA cos B=(abc)/(4R^(2))

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  6. (vii) (b^(2) -c^(2)) cos 2A + (c^(2) -a^(2)) cos 2B + (a^(2) -b^(2)) c...

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  7. (viii) (b^(2) -c^(2)) cos 2A + (c^(2)-a^(2)) cos 2B + (a^(2)-b^(2)) co...

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  8. (ix) (a^(2) sin (B-C))/(sinA) + (b^(2) sin (C-A))/(sin B) + (c^(2) sin...

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  9. (x) (a sin(B-C))/(b^(2)-c^(2)) = (b sin (C-A))/(c^(2)-a^(2)) = (c sin(...

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  10. (xi) a^(2) sin 2B + b^(2) sin 2A = 4Delta

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  11. (xii) (b+c-a)(cot 'B/2' + cot 'C/2') = 2a cot 'A/2

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  12. (xiii) a^(3) sin (B-C) + b^(3) sin (C-A) + c^(3) sin(A-B)=0

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  13. (xiv) a cos A + b cos B + c cos C = (abc)/(2R^(2))

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  14. (xv) a cos (B-C) + b cos (C-A) + c cos (A-B) = (4(Delta))/R

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  15. If C=60^(@), show that, 2a-b = 2 c cosB

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  16. If b+c=2a, show that, 2sin 'A/2' = sin (B+A/2)

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  17. If a cos^(2)'C/2' + c cos^(2)'A/2' = (3b)/2 then show that the sides o...

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  18. In any triangle ABC, if 1/(a+c) + 1/(b+c) = 3/(a+b+c) then show that, ...

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  19. If 2 cos A = (sin B)/(sin C) then show that the triangle is isosceles.

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  20. In triangle ABC ,a=2,b=sqrt3 and A=90^@, then find B?

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