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If in a triangle A B C ,cosA+2cosB+cosC=...

If in a triangle `A B C ,cosA+2cosB+cosC=2` prove that the sides of the triangle are in `AP`

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To prove that the sides of triangle \( ABC \) are in Arithmetic Progression (AP) given that \( \cos A + 2 \cos B + \cos C = 2 \), we will follow these steps: ### Step 1: Rearranging the equation We start with the equation: \[ \cos A + 2 \cos B + \cos C = 2 \] Rearranging gives: ...
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RD SHARMA ENGLISH-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-All Questions
  1. With usual notations, if in a triangle A B C(b+c)/(11)=(c+a)/(12)=(a+b...

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  2. If a^2,b^2,c^2 are in A.P., prove that cotA ,cotB ,cotC are in AdotPdo...

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  3. If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the ...

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  4. In a triangle A B C ,/C=60^0, then prove that: 1/(a+c)+1/(b+c)=3/(a+b+...

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  5. Prove that b(c cosA-acosC)=c^2-a^2

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  6. 2(bc cosA+c acosB+a bcosC)=a^2+b^2+c^2

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  7. In a A B C , if /B=60^0 , prove that (a+b+c)(a-b+c)=3c a

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  8. In any DeltaABC , prove that: (sinB)/(sinC)=(c-acosB)/(b-acosC)

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  9. In any A B C , prove that: 2{asin^2C/2+csin^2A/2}=a+c-b

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  10. In any A B C , prove that: 2{b cos^2(C/2) + c cos^2(B/2)}=a+c+b

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  11. In any A B C , prove that: (b+c)cos A+(c+a)cos B+(a+b)cos C=a+b+c

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

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  13. In a Delta A B C ,if a=2,/B=60^0a n d/C=75^0 , then b= (a)sqrt(3) ...

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  14. If a^2,b^2,c^2 are in A.P., prove that cotA ,cotB ,cotC are in AdotPdo...

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  15. In any triangle A B C , prove that: (1+cos(A-B)cos C)/(1+cos(A-C)cos B...

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  16. In any triangle. if(a^2-b^2)/(a^2+b^2)=("sin"(A-B))/("sin"(A+B)) , the...

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  17. For any triangle ABC, prove that acosA+bcosB+ccosC=2asinBsinC

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

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

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  20. In a triangle A B C , if acosA=bcosB , show that the triangle is eithe...

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