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If cot A/2:cot"" B/2: cot"" C/2 = 3:5:7 ...

If `cot A/2:cot"" B/2: cot"" C/2 = 3:5:7` then show that `a:b:c = 6:5:4`.

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SRISIRI PUBLICATION-PROPERTIES OF TRIANGLES-SAQ (1D STAR Q)
  1. Show that (cosA)/(a)+(cosB)/(b)+(cosC)/(c)=(a^(2)+b^(2)+c^(2))/(2abc)

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  2. Prove that (a)/(bc)+(cosA)/(a)=(b)/(ca)+(cosB)/(b)=(c)/(ab)+(cosC)/(c)

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  3. Prove that cotA+cotB+cotC=(a^2+b^2+c^2)/(4Delta)

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  4. In DeltaABC, " if" (1)/(a+c)+(1)/(b+c)=(3)/(a+b+c) then show that C=...

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  5. If C=60^(@), " then show that"(a)/(b+c)+(b)/(c+a)=1

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  6. In a DeltaABC" if " a:b:c=7:8:9 then show that cosA:cosB:cosC=14:11:6

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  7. Show that a^(2)cotA+b^(2)cotB+c^(2)cotC=(abc)/(R)

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  8. Prove that (1+cos(A-B)cosC)/(1+cos(A-C)cosB)=(a^(2)+b^(2))/(a^(2)+c^(2...

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  9. Show that b^(2)sin2C+c^(2)sin2B=2bcsinA

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  10. In a DeltaABC " if " a cosA=bcosB the prove that triangle is either...

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  11. In DeltaABC show that (a+b+c)(tan.(A)/(2)+tan.(B)/(2))=2cot.(C)/(2)

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  12. If cot A/2:cot"" B/2: cot"" C/2 = 3:5:7 then show that a:b:c = 6:5:4.

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  13. Prove that cot.(A)/(2)+cot.(B)/(2)+cot.(C)/(2)=(s^(2))/(Delta)

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  14. Prove that tan.(A)/(2)+tan.(B)/(2)+tan.(C)/(2)=(bc+ca+ab-s^(2))/(Delta...

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  15. If cot.(A)/(2)+cot.(B)/(2)+cot.(C)/(2) are in A.P , then prove that a,...

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  16. If sin^(2).(A)/(2)+sin^(2).(B)/(2)+sin^(2).(C)/(2) are in H.P , show t...

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  17. In DeltaABC prove that tan((B-C)/(2))=(b-c)/(b+c)cot.(A)/(2)

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  18. Show that (1)/(r^(2))+(1)/(r(1)^(2))+(1)/(r(2)^(2))+(1)/(r(3)^(2))=(a^...

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