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

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

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Prove that a^(2) sin 2B + b^(2) sin 2A = 4 Delta

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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

In a triangle ABC, if a, b, c are in A.P. and (b)/(c) sin 2C + (c)/(b) sin 2B + (b)/(a) sin 2A + (a)/(b) sin 2B = 2 , then find the value of sin B

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(i) If in a triangle ABC, a^(4) + b^(4) +c^(4) - 2b^(2) c^(2) -2c^(2)a^(2)=0 , then show that, C=45^(@) or 135^(@) . (ii) In in a triangle ABC, sin^(4)A + sin^(4)B + sin^(4)C = sin^(2)B sin^(2)C + 2sin^(2) C sin^(2)A + 2sin^(2)A sin^(2)B , show that, one of the angles of the triangle is 30^(@) or 150^(@)

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If (a^(2) + b^(2))sin (A-B) = (a^(2)-b^(2)) sin(A+B) then show that, the triangle is either isoscelels or right angled.

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CHHAYA PUBLICATION-PROPERTIES OF TRIANGLE -Short Answer Type Questions
  1. (ix) (a^(2) sin (B-C))/(sinA) + (b^(2) sin (C-A))/(sin B) + (c^(2) sin...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If A,B,C be the angles ofa triangle then prove that (sin A + sin B)(si...

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  20. In any triangle ABC, if sin^(2)A + sin^(2)B + sin^(2)C = 9/4, show tha...

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