Home
Class 11
MATHS
Show that: sin(B-C)cos(A-D)+sin(C-A)co...

Show that:
`sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0`

Text Solution

Verified by Experts

Here, we will use,
`2sinAcosB = sin(A+B)+sin(A-B)`
Now,
`L.H.S. = sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(a-B)cos(C-D)`
`=1/2[2sin(B-C)cos(A-D)+2sin(C-A)cos(B-D)+2sin(A-B)cos(C-D)]`
`=1/2[sin(B-C+A-D)+sin(B-C-A+D)+sin(C-A+B-D)+sin(C-A-B+D)+sin(A-B+C-D)+sin(A-B-C+D)]`
`=1/2[sin(B-C+A-D)-sin(A-B+C-D)-sin(A-B-C+D)-sin(A+B-C-D)+sin(A-B+C-D)+sin(A-B-C+D)]`
`=1/2[0]`
...
Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    RD SHARMA ENGLISH|Exercise All Questions|493 Videos

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|120 Videos

Similar Questions

Explore conceptually related problems

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

Prove that: a) sin(A+B+C) + sin(A-B-C)+sin(A+B-C) + sin(A-B+C) = 4sinAcosBcosC b) cos(A+B+C)+cos(A+B-C)+cos(B+C-A)+cos(C+A-B)=4cosAcosBcosC

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

In any quadrilateral ABCD, prove that: i) sin(A+B)+sin(C+D)=0 ii) cos(A+D)-cos(B+C)=0

If A+B+C=pi , prove that : (sin ((B+C)/(2)) + sin ((C+A)/(2)) + sin( (A+B)/(2) )) equals (4cos ((pi-A)/(4)) cos( (pi-B)/(4)) cos((pi-C)/(4))) .

Statement:1 If cos(A+B)sin( C +D) = cos(A-B) sin(C-D) , then the values of cotAcotBcotC is cotD. And Statement:2: If cos(A+B) sin(C+D)= cos(A-B) sin(C-D) then the value of tanAtanBtanC is tanD.

In a DeltaA B C ,\ prove that , sin^3Acos(B-C)+sin^3B cos(C-A)+sin^3\ C cos(A-B) = 3\ sin A\ sin B \ sin C

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: (cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B+C)+sin(-A+B+C)+sin(A-B+C)-"sin"(A+B-C))=cot C

RD SHARMA ENGLISH-TRANSFORMATION FORMULAE-All Questions
  1. Show that: sinAsin(B-C)+sinB sin(C-A)+sinCsin(A-B)=0

    Text Solution

    |

  2. Show that: sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0

    Text Solution

    |

  3. If t a nalpha=x/(x+1) and t a nbeta=1/(2x+1) , then alpha+beta is equa...

    Text Solution

    |

  4. If msintheta=n sin(theta+2alpha), prove that tan(theta+alpha)cotalpha...

    Text Solution

    |

  5. If sin(B+C-A),sin(C+A-B),sin(A+B-C), are AdotPdot,t h e ncot A ,cot B ...

    Text Solution

    |

  6. If cos(alpha+beta)*sin(gamma+delta)=cos(alpha-beta)*sin(gamma-delta), ...

    Text Solution

    |

  7. If xcostheta=ycos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , prove that x y...

    Text Solution

    |

  8. If cos e cA+secA=cos e c B+s e cB , prove that: "tanAtanB"=cot(A+B)/2

    Text Solution

    |

  9. If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma...

    Text Solution

    |

  10. If cos A+cosB=1/2 and sin A+ sinB=1/4 , prove that: tan((A+B)/2)=1/2

    Text Solution

    |

  11. If asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(4pi)/3) , prove that ...

    Text Solution

    |

  12. If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany ...

    Text Solution

    |

  13. Prove that: tan20^0tan40^0tan80^0=tan60^0

    Text Solution

    |

  14. Prove that :"sin"Asin(60^0-A)sin(60^0+A)=1/4sin3A

    Text Solution

    |

  15. Show that: t a n(60^0+theta)t a n(60^0-theta)=(2cos2theta+1)/(2cos2the...

    Text Solution

    |

  16. If alpha+beta=90^0 , find the maximum and minimum values of sinalphas...

    Text Solution

    |

  17. Prove that: cos20^0cos40^0cos60^0cos80^0=1/(16)

    Text Solution

    |

  18. Prove that: sin20^0sin40^0sin60^0sin80^0=3/(16)

    Text Solution

    |

  19. Prove that: 4"cos"12^0cos48^0cos72^0=cos36^0

    Text Solution

    |

  20. Prove that: tantheta.tan(60^0-theta).tan(60^0+theta)=tan3thetadot.'

    Text Solution

    |