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(ix) (a^(2) sin (B-C))/(sinA) + (b^(2) s...

(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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In any triangle ABC, prove that (a^(2)sin(B-C))/(sin B + sinC) + (b^(2)sin(C-A))/(sinC + sinA) +(c^(2)sin(A-B))/(sinA + sinB)=0

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

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

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

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

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In triangle ABC, (i) asin(A/2 + B) = (b+c) sin A/2

CHHAYA PUBLICATION-PROPERTIES OF TRIANGLE -Short Answer Type Questions
  1. (vii) (b^(2) -c^(2)) cos 2A + (c^(2) -a^(2)) cos 2B + (a^(2) -b^(2)) c...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. In any triangle ABC, if cosA cos B + sin A sin B sinC =1 then prove th...

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  17. In any triangle ABC, prove that cosA + cos B + cos C le 3/2

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  18. In any triangle ABC, show that (a sin C)/(b - a cosC)= tanA.

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  19. If B=30^(@), b=3sqrt(2)-sqrt(6), c=6-2sqrt(3), solve the triangle.

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  20. In any triangle ABC, if cosA + cos B + cosC =3/2, then show that the t...

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