Home
Class 12
MATHS
Prove the following : cos(A-D)sin(B-C)+c...

Prove the following : `cos(A-D)sin(B-C)+cos(B-D)sin(C-A)+cos(C-D)sin(A-B) = 0`

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MBD PUBLICATION|Exercise QUESTION BANK|523 Videos

  • VECTORS

    MBD PUBLICATION|Exercise QUESTION BANK|138 Videos

Similar Questions

Explore conceptually related problems

Prove the cosA.sinB(B-C) + cosB.sin(C-A) + cosC.sin(A-B) = 0

Prove the following : cos(A+B)+sin(A-B) 2sin( 45^@ +A)cos( 45^@ +B)

Prove the following : cos^6A-sin^6A = cos2A(1-1/4 sin^2 2A)

Prove the following : (sin(A+B)+cos(A-B))/(sin(A-B)+cos(A+B)) = sec2B+tan2B

Prove the following : sin2A+sin2B+sin2C-sin2(A+B+C) 4sin(B+C)sin(C+A)sin(A+B)

Prove the following : sin2A+sin2B+sin2(A-B) = 4sinA.cosB.cos(A-B)

Prove the following : (1-cos2A+sin2A)/(1+cos2A+sin2A) = tanA

Prove the sinA.sin(B-C) + sinB.sin(C-A) + sinC.sin(A-B) = 0

Prove the following : cos2A+cos2B+cos2(A-B)+1 = 4cosA.cosB.cos(A-B)

Prove the following : sinA-sin3A+sin5A = sin3A(2cos2A-1)

MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. If A+B+C=pi and cosA=cosB.cosC show that tanB+tanC=tanA

    Text Solution

    |

  2. If A+B+C=pi and cosA=cosB.cosC show that 2cotB.cotC=1

    Text Solution

    |

  3. Prove the following : cos(A-D)sin(B-C)+cos(B-D)sin(C-A)+cos(C-D)sin(A-...

    Text Solution

    |

  4. Prove the following : sin2A+sin2B+sin2(A-B) = 4sinA.cosB.cos(A-B)

    Text Solution

    |

  5. Prove the following : cos2A+cos2B+cos2(A-B)+1 = 4cosA.cosB.cos(A-B)

    Text Solution

    |

  6. Prove the following : sin2A+sin2B+sin2C-sin2(A+B+C) 4sin(B+C)sin(C+A...

    Text Solution

    |

  7. Prove the following : sinA+sin3A+sin5A =sin3A(1+2cos2A)

    Text Solution

    |

  8. Prove the following : sinA-sin3A+sin5A = sin3A(2cos2A-1)

    Text Solution

    |

  9. Prove the following : cos(A+B)+sin(A-B) 2sin(45^@+A)cos(45^@+B)

    Text Solution

    |

  10. Prove the following : cos4A-cos4B = 8(cosA-cosB)(cosA+cosB)(cosA-sin...

    Text Solution

    |

  11. Prove the following : (1-tan^2(45^@-A))/(1+tan^2(45^@-A)) = sin2A

    Text Solution

    |

  12. Prove the following : (cosA+sinA)/(cosA-sinA)-(cosA-sinA)/(cosA+sinA) ...

    Text Solution

    |

  13. Prove the following : (1-cos2A+sin2A)/(1+cos2A+sin2A) = tanA

    Text Solution

    |

  14. Prove the following : (sin(A+B)+cos(A-B))/(sin(A-B)+cos(A+B)) = sec2...

    Text Solution

    |

  15. Prove the following : (cos7alpha+cos3alpha-cos5alpha-cosalpha)/(sin7al...

    Text Solution

    |

  16. Prove the following : (sintheta+sin3theta+sin5theta+sin7theta)/(costhe...

    Text Solution

    |

  17. Prove the following : Express 4cosA.cosB.cosC as the sum of four cosin...

    Text Solution

    |

  18. Express cos2A+cos2B+cos2C+cos2(A+B+C) as the product of three cosines.

    Text Solution

    |

  19. Prove the following : cos^6A-sin^6A = cos2A(1-1/4 sin^2 2A)

    Text Solution

    |

  20. Prove the following : cos^6A+sin^6A = 1/4 (1+3 cos^2 2A)

    Text Solution

    |