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In any triangle A B C , prove that: (a^2...

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

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MAHAVEER PUBLICATION-PROPERTIES OF TRIANGLES-QUESTION BANK
  1. In triangle ABC , prove that (b+c)cos A +(c+a)cos B +(a+b)cos C=a+b+c.

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  2. If a=3,b=4 and c=5, find cos A, cos B and cos C.

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  3. The sides of a triangle are 8 cm, 10 cm and 12 cm, find the greatest a...

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  4. The sides of a triangle are 3 cm, 5 cm and 7 cm. Find the greatest ang...

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  5. A triangle side are few 7 cm, 4sqrt3 cm and sqrt(13) cm then the smal...

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  6. In any triangle ABC, ifangle C=90^@, AC=4 unit, BC=3, find AB.

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  7. For any triangle ABC, prove that(a+b)/c=(cos((A-B)/2))/(sinC/2)

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  8. For any triangle ABC, prove that(a-b)/c=(sin((A-B)/2))/(cosC/2)

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  9. In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

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  10. For any triangle ABC, prove that a(bcosC-ccosB)=b^2-c^2

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  11. In DeltaABC, prove that: a(cosC-cosB)=2(b-c)cos^(2)A/2

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  12. In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

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  13. In any triangle A B C , prove that: ("sin"(B-C))/("sin"(B+C))=(b^2-c^2...

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  14. In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

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  15. In any triangle A B C , prove that: (b-c)cot A/2+(c-a)cot B/2+(a-b)cot...

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  16. In any triangle A B C , prove that: \ a^3sin(B-C)+b^3sin(C-A)+c^3sin(A...

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  17. For any triangle ABC, prove that(cosA)/a+(cosB)/b+(cosC)/c=(a^2+b^2+c^...

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  18. In any DeltaABC, prove that ((b^(2)-c^(2)))/a^(2)"sin 2a"+((c^(2)-a^(2...

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  19. For any triangle ABC, prove that (b^2 c^2)"\ cot"A"\ "+"\ "(c^2 a^2)"\...

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  20. In any triangle A B C , prove that: (a^2sin(B-C))/(sinB+s in C)+(b^2si...

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