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In any DeltaABC, prove that a^(3)cos(B-...

In any `DeltaABC`, prove that
`a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)=3abc`

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ICSE-PROPERTIES OF TRIANGLE-EXERCISE 7
  1. In any DeltaABC, prove that (cos2A)/a^(2)-(cos2B)/b^(2)=1/a^(2)-1/b^...

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  2. In any DeltaABC, prove that (1+cos(A-B)cosC)/(1+cos(A-C)cosB)=(a^(2)...

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  3. In any DeltaABC, prove that (b^(2)-c^(2))cotA+(c^(2)-a^(2))cotB+(a^(...

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  4. In any DeltaABC, prove that a^(3)sin(B-C)cosec^(2)A+b^(3)sin(C-A)cos...

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  5. In any DeltaABC, prove that a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)...

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  6. In a DeltaABC, if (2cosA)/a+(cosB)/b+(2cosC)/c=a/(bc)+b/(ca), prove th...

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  7. In a DeltaABC, AD is the altitude from A. Given b gt c, angleC=23^(@)"...

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  8. In DeltaABC, (a^(2)+b^(2))/(a^(2)-b^(2))=(sin(A+B))/(sin(A-B)), prove ...

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  9. If (sinA)/(sinC)=(sin(A-B))/(sin(B-C)), prove that a^(2), b^(2), c^(2)...

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  10. If sin2A+sin2B=sin2C, prove that A=90^(@)" or " B=90^(@).

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  11. If in a triangle A B C ,/C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+...

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  12. In a DeltaABC the angles A, B, C are in A.P. show that 2cos""(A-C)/2=(...

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  13. If the angles A, B, C of DeltaABC are in A.P. and b:c=sqrt(3):sqrt(2),...

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  14. If A=45^(@) and B=75^(@), show that a+csqrt(2)=2b.

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  15. The angles A, B, C of a triangle are in the ratio 3:5:4, prove that a+...

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  16. In a DeltaABC, if cosA=17/22, cosC=1/14, prove that the ratio of the s...

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  17. The angle of a triangle are in the ratio 1 : 2 : 7, prove that the rat...

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  18. If the sides of DeltaABC in the ratio 4 : 5 : 6, prove that one angle ...

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  19. Two sides and included angles of a triangle are respectively 3+sqrt(3)...

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  20. In a DeltaABC, if B=3C, prove that (i) cosC=sqrt(((b+c)/(4c)))" (i...

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