Home
Class 11
MATHS
cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2...

`cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2`

Text Solution

Verified by Experts

`L.H.S. = (cos2A)/a^2-(cos2B)/b^2`
`=(1-2sin^2A)/a^2 - (1-2sin^2b)/b^2`
`=1/a^2-1/b^2-2(sin^2A/a^2 - sin^2B/b^2)`
From sine law,
`sinA/a = sinB/b = sinC /c`
`:. sin^2A/a^2 = sin^2B/b^2 `
`:. 1/a^2-1/b^2-2(sin^2A/a^2 - sin^2B/b^2) = 1/a^2-1/b^2-2(0)`
`1/a^2-1/b^2 = R.H.S.`
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 DeltaABC , prove that (cos2A)/a^(2)-(cos2B)/b^(2)=1/a^(2)-1/b^(2)

In A B C Prove that cos^2A/2+cos^2B/2+cos^2C/2lt=9/4dot If cos^2A/2+cos^2B/2+cos^2C/2=y(x^2+1/(x^2)) then find the maximum value of ydot

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

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

If sin^(-1)((2a)/(1+a^2))-cos^(-1)((1-b^2)/(1+b^2))=tan^(-1)((2x)/(1-x^2)) , then prove that x=(a-b)/(1+a b)

Prove that b^(2) cos 2 A - a^(2) cos 2B = b^(2) -a^(2)

In any DeltaABC , prove that (1+cos(A-B)cosC)/(1+cos(A-C)cosB)=(a^(2)+b^(2))/(a^(2)+c^(2))

In any triangle A B C , prove that: (1+cos(A-B)cos C)/(1+cos(A-C)cos B)=(a^2+b^2)/(a^2+c^2)

In any triangle A B C , prove that: (1+cos(A-B)cos C)/(1+cos(A-C)cos B)=(a^2+b^2)/(a^2+c^2)

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

RD SHARMA ENGLISH-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-All Questions
  1. a(cosC-cosB)=2(b-c)cos^2A/2

    Text Solution

    |

  2. a^2(cos^2B-cos^2C)+b^2(cos^2C-cos^2A)+c^2(cos^2A-cos^2B)=0 .

    Text Solution

    |

  3. cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2

    Text Solution

    |

  4. In a Delta A B C ,\ if\ a=2,\ b=3\ a n d\ sin A=2/3 then find /B

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. In any triangle A B C , prove that: \ a^3sin(B-C)+b^3sin(C-A)+c^3sin(A...

    Text Solution

    |

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

    Text Solution

    |

  9. In any triangle A B C , prove that: (b-c)/(b+c)=(tan((B-C)/2))/(tan((B...

    Text Solution

    |

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

    Text Solution

    |

  11. A tree stands vertically on a hill side which makes an angle of 15^0 w...

    Text Solution

    |

  12. A person, standing on the bank of a river, observes that the angle sub...

    Text Solution

    |

  13. The angle of elevation of to be top point P of the vertical tower PQ o...

    Text Solution

    |

  14. The elevation of a tower at a station A due North of it is alpha and ...

    Text Solution

    |

  15. If in a Delta A B C ,\ /A=45^0,\ /B=60^0,\ a n d\ /C=75^0 , find the ...

    Text Solution

    |

  16. If in any Delta A B C ,\ /C=105^0,/B=45^0, a=2, then find bdot

    Text Solution

    |

  17. In Delta A B C ,\ if\ a=18 ,\ b=24\ a n d\ c=30\ a n d\ /C=90^0 find ...

    Text Solution

    |

  18. In any triangle A B C , prove that following : (a-b)/(a+b)=(tan((A-B)/...

    Text Solution

    |

  19. In any triangle A B C , prove that following : (a-b)cosC/2\ = csin((A-...

    Text Solution

    |

  20. In any triangle A B C , prove that following : c/(a-b)=(tan(A/2)+tan(B...

    Text Solution

    |