Home
Class 11
MATHS
b(cosA-acosC)=c^2-a^2...

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

Text Solution

Verified by Experts

L.H.S=`b(c cosA-acosC)`
from projction formula
`b=(c cosA+acosC)...(i)`
so by (i) `(c cosA+acosC)(c cosA-acosC)`
=`(c^2 cos^2A-a^2 cos^2C)`
=`c^2(1-sin^2A)-a^2(1-sin^2C)`
=`c^2-a^2-c^2sin^2A+a^2sin^2C`
by sine law,
...
Promotional Banner

Topper's Solved these Questions

  • SETS

    RD SHARMA|Exercise Solved Examples And Exercises|218 Videos

  • SOME SPECIAL SERIES

    RD SHARMA|Exercise Solved Examples And Exercises|69 Videos

Similar Questions

Explore conceptually related problems

In DeltaABC , prove that: b(cosA-cosC)=2(c-a)cos^(2)B/2

(b^2-c^2)/(cos B+cosC)+(c^2-a^2)/(cosC+cosA)+(a^2-b^2)/(cosA+cosB)=……

In DeltaABC , prove that: c(acosB-b cosA)=a^(2)-b^(2)

In a triangle ABC , with usual notations , prove that (a-bcosC)/(b-acosC)=(cosB)/(cosA) .

If A+B+C= 360^(@) ,prove that: 1-cos^(2)A-cos^(2)B-cos^(2)C+2cosA cos B cos C=0

Which of the following holds goods for any tiangle ABC, a,b,c are the lengths of the sides R is circumradius (A) (cosA)/a+(cosB)/b+(cosC)/c= (a^2+b^2+c^2)/(2abc) (B) (sinA)/a+(sinB)/b+(sinC)/c=3/(2R0 (C) (cosA)/a=(cosB)/b=(cosC)/c (D) (sin2A)/a62=(sin2B)/b^2=(sin2C)/c^2

If cot A=(b)/(a) ,then prove that : (asin - b cosA)/(sin A+bcosA)=(a^(2)-b^(2))/(a^(2)+b^(2))

In any DeltaABC , prove that ac cosB-bc cosA=(a^(2)-b^(2))

ln a DeltaABC , if (cosA)/a=(cosB)/b=(cosC)/c and the side a = 2, then area of the triangle is

In a triangle ABC , if a,b,c are the sides opposite to angles A , B , C respectively, then the value of |{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}| is

RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
  1. If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. 2(bc cosA+c acosB+a bcosC)=a^2+b^2+c^2

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |