Home
Class 11
MATHS
In any A B C , prove that: 2{asin^2C/2+...

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

Text Solution

AI Generated Solution

To prove the equation \( 2\left(a \sin^2\frac{C}{2} + c \sin^2\frac{A}{2}\right) = a + c - b \) in any triangle \( ABC \), we will follow these steps: ### Step 1: Use the double angle identity for sine We know that: \[ 2 \sin^2 x = 1 - \cos 2x \] Applying this identity, we can rewrite the left-hand side (LHS): ...
Promotional Banner

Topper's Solved these Questions

  • SETS

    RD SHARMA ENGLISH|Exercise All Questions|228 Videos

  • SOME SPECIAL SERIES

    RD SHARMA ENGLISH|Exercise All Questions|69 Videos

Similar Questions

Explore conceptually related problems

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

In DeltaABC , prove that: 2[asin^(2)B/2+bsin^(2)A/2]=a+b-c

In any DeltaABC , prove that asin(A/2+B)=(b+c)sin""A/2

In any triangle A B C , prove that: \ asin(B-C)+b sin(C-A)+csin(A-B)=0

In a DeltaABC,2asin^(2)C/2+2csin^(2)A/2=

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

In any DeltaABC , prove that : (b-c)/a cos^2 (A/2) + (c-a)/b cos^2 (B/2) + (a-b)/c cos^2 (C/2) = 0

In any Delta A B C , prove that: a(b\ cos C-c cosB)=b^2-c^2

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

In any DeltaABC , prove that : (cos^2(A/2))/a + (cos^2(B/2))/b + (cos^2(C/2))/c = s^2/(abc)

RD SHARMA ENGLISH-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-All Questions
  1. In a A B C , if /B=60^0 , prove that (a+b+c)(a-b+c)=3c a

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. The angles of a triangle A B C are in AdotPdot and it is being given t...

    Text Solution

    |

  19. In A B C , prove that (a-b^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

    Text Solution

    |

  20. In a A B C , if a=3,b=5a n dc=7,fin dcos A ,cos Ba n dcos Cdot

    Text Solution

    |