Home
Class 11
MATHS
Prove that: (sin A+sin B)/(cos A+cos B)=...

Prove that: `(sin A+sin B)/(cos A+cos B)=tan((A+B)/2)`

Text Solution

Verified by Experts

`LHS :`

`frac{sin A+sin B}{cos A+cos B}`

`=frac{2 sin (frac{A+B}{2}) cos (frac{A-B}{2})}{2 cos (frac{A+B}{2}) cos (frac{A-B}{2})}`

...
Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    RD SHARMA|Exercise Solved Examples And Exercises|488 Videos

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos

Similar Questions

Explore conceptually related problems

Prove that (sin A+sin B)/(cos A+cos B)+(cos A-cos B)/(sin A-sin B)=0

Prove that ((sin 2A -sin 2B)/(cos2A + cos 2B))^(n) + ((cos 2A - Cos 2B)/(sin 2A + sin 2B))^(n) = 2 tan^(n) (A-B) or 0 According as n is even or n is odd.

Prove that : (sin 2A+sin 2B + sin 2C)/(cos A + cos B + cos C-1) = 8 cos(A/2) cos( B/2) cos( C/2)

Prove that (1 + sin A) / (cos A) + (cos B) / (1-sin B) = (2sin A-2sin B) / (sin (AB) + cos A-cos B)

Prove that: ("sin"(A-B))/(cos A cosB)+(sin(B-C))/(cos B cos C)+("sin"(C-A))/(cos C cos A)=0

Prove that: (sin(A+B)+sin(A-B))/(cos(A+B)+cos(A-B))=tan A

prove that ((cos A+cos B)/(sin A-sin B))^(n)+((sin A+sin B)/(cos A-cos B))^(n)=2cot^(n)((A-B)/(2)),n is even

Prove that: ((cos A+cos B)/(sin A-sin B))^(n)+((sin A+sin B)/(cos A-cos B))^(n)={2cot^(n)((A-B)/(2)),quad if niseven0,if nisodd

Prove that: (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

Prove each of the following identities : ((sin A - sin B))/((cos A + cos B)) + (( cos A - cos B))/((sin A + sin B)) =0

RD SHARMA-TRANSFORMATION FORMULAE-Solved Examples And Exercises
  1. Prove that: sin20^0sin40^0sin60^0sin80^0=3/(16)

    Text Solution

    |

  2. Prove that: (sin 5A-sin 3A)/(cos5A+cos3A)=t a n A

    Text Solution

    |

  3. Prove that: (sin A+sin B)/(cos A+cos B)=tan((A+B)/2)

    Text Solution

    |

  4. (sinA+sin3A)/(cosA+cos3A)=tan2A

    Text Solution

    |

  5. Prove that: (cos7A+cos5A)/(sin7A-sin5A)=cot A

    Text Solution

    |

  6. Prove that: (cos9x-cos5x)/(sin 17 x-sin3x)=\ -(sin2x)/(cos 10 x)

    Text Solution

    |

  7. Prove that: (sin5x+sin3x)/(cos5x+cos3x)=t a n4x

    Text Solution

    |

  8. Prove that cot4x(sin5x+sin3x)=cot x(sin5x-sin3x)

    Text Solution

    |

  9. Prove that : sin x+sin3x+sin5x+sin7x=4cos x\ cos2xsin4x

    Text Solution

    |

  10. Prove that:\ (sin3A+sin A)sin A+(cos3A-cos A)cos A=0

    Text Solution

    |

  11. show that cos2thetacos(theta/2)-cos3thetacos(9theta/2)=sin5thetasin(5t...

    Text Solution

    |

  12. Prove that: (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-be...

    Text Solution

    |

  13. Prove that: (cosalpha-cosbeta)^2+(sinalpha-sinbeta)^2=4sin^2((alpha-be...

    Text Solution

    |

  14. Prove that: cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos(alp...

    Text Solution

    |

  15. Prove that: (cos4x+cos3x+cos2x)/(sin4x+sin3x+sin2x)=cot3x

    Text Solution

    |

  16. Prove that: (cos2A\ cos3A-cos2Acos7A+cos10 A cos A)/(sin4A\ sin3A-sin2...

    Text Solution

    |

  17. If three angles A, B, and C are in A.P. prove that: cot B=(sin A-sin C...

    Text Solution

    |

  18. Prove that: (cos6theta+6cos4theta+15 cos2theta+10)/(cos5theta+5cos3the...

    Text Solution

    |

  19. Express each of the following as the product of sines and cosines: sin...

    Text Solution

    |

  20. Express each of the following as the product of sines and cosines: cos...

    Text Solution

    |