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

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

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To prove the equation \( 2(bc \cos A + ca \cos B + ab \cos C) = a^2 + b^2 + c^2 \), we will start with the left-hand side (LHS) and manipulate it using the cosine rule. ### Step 1: Write down the LHS We start with the left-hand side of the equation: \[ LHS = 2(bc \cos A + ca \cos B + ab \cos C) \] ...
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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
  1. In a triangle A B C ,/C=60^@, then prove that: 1/(a+c)+1/(b+c)=3/(a+b+...

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

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  3. 2(bc cosA+c acosB+a bcosC)=a^2+b^2+c^2

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

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

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

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  7. 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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  8. 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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  9. For any triangle ABC, prove that a(bcosC-c cosB)=b^2-c^2

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

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

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

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  13. If in a A B C ,(a^2-b^2)/(a^2+b^2)=(sin(A-B))/(sin(A+B) , prove that ...

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  14. In any triangle A B C , prove that: acosA+bcosB+c cosC=2asinBsinC

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  15. In any triangle A B C , (b-c)cot A/2+(c-a)cot B/2+(a-b)cot C/2 =0

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

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

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  18. If in triangle the angles are in the ratio as 1:2:3 , prove that the ...

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  19. In the sides of a triangle are in the ratio 1:sqrt(3):2, then the meas...

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

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