Home
Class 11
MATHS
In quadrilateral A B C D , if sin((A+B)/...

In quadrilateral `A B C D ,` if `sin((A+B)/2)cos((A-B)/2)+"sin"((C+D)/2)cos((C-D)/2)=2` then find the value of `sinA/2sinB/2sinC/2sinD/2dot`

Text Solution

Verified by Experts

`1/2[2sin((A+B)/2)cos((A-B)/2)+2sin((C+D)/2)cos((C-D)/2)]=2`
`2sinCcosD=sin(C+D)+sin(C-D)`
`sinA+sinB+sinC+sinD=4`
`sinA-11=sinB=sinC=sinD`
`A=pi/2=B=C=D`
`sin(A/2)sin(B/2)sin(C/2)sin(D/2)`
`=sin^4pi/4=(1/sqrt2)^4=1/4`.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

ln a quadrilateral ABCD if sin((A+B)/2)cos((A-B)/2)+sin((C+D)/2)cos((C-D)/2)=2, then sin(A/2)sin(B/2)sin(C/2)sin(D/2) has the value equal to (a)1/8 (b)1/4 (c)1/(2sqrt2) (d)1/2

If cos(A+B+C)=cos A cos B cos C, then find the value of (8sin(B+C)sin(C+A)sin(A+B))/(sin2A sin2sin2C)

In a quadrilateral if (sin (A + B)) / (2) (cos (AB)) / (2) + (sin (c + D)) / (2) + (sin (c + D)) / ( 2) (cos (cD)) / (2) = 2, then (cos A) / (2) (cos B) / (2) + (cos A) / (2) (cos c) / (2) + (cos A) / (2) (cos D) / (2) + (cos B) / (2) (cos C) / (2) + (cos B) / (2) (cos D) / (2) + (cos C) / (2) (cos D) / (2)

If A+B+C=pi then prove cos( (A)/2) cos( (B-C)/2) + cos( B/2) cos((C-A)/2) + cos( C/2) cos( (A-B)/2) = sinA +sinB+sinC

If A,B,C and D are angles of quadrilateral and sin(A)/(2)sin(B)/(2)sin(C)/(2)sin(D)/(2)=(1)/(4) , prove that A=B=C=D= pi//2

If ABC D is a cyclic quadrilateral, then find the value of sinA+sinB-sinC-sinD If A+B+C=(pi)/(2) , then find the value of tanA tanB+tanBtanC+tanC tanA

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.

Prove (i)sin C+sin D=2(sin(C+D))/(2)(cos(C-D))/(2)(ii)sin C-sin D=2(sin(C-D))/(2)(cos(C+D))/(2)

In a triangle ABC if (sin2A+sin2B+sin2C)/(cos A+cos B+cos C-1)=((lambda)/(2))cos((A)/(2))cos((B)/(2))cos((C)/(2)) then lambda equals

In Delta ABC If,(sin^(2)A+sin^(2)B+sin^(2)C)/(cos^(2)A+cos^(2)B+cos^(2)C)=2 Then the triangle is

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. ABC is an acute angled triangle with circumcenter O and orthocentre H....

    Text Solution

    |

  2. If sintheta=1/2a n dcostheta=-(sqrt(3))/2, then the general value of ...

    Text Solution

    |

  3. In quadrilateral A B C D , if sin((A+B)/2)cos((A-B)/2)+"sin"((C+D)/2)c...

    Text Solution

    |

  4. Find the range of y=sin^3x-6sin^2x+11sinx-6.

    Text Solution

    |

  5. A ladder rest against a wall making an angle alpha with the horizontal...

    Text Solution

    |

  6. Let ABC be an acute angled triangle whose orthocentre is at H. If a...

    Text Solution

    |

  7. The most general value for which tantheta=-1 and costheta=1/(sqrt(2)) ...

    Text Solution

    |

  8. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

    Text Solution

    |

  9. Prove that: cos18^0-s in 18^0=sqrt(2)sin27^0

    Text Solution

    |

  10. In a acute angled triangle ABC, proint D, E and F are the feet of the ...

    Text Solution

    |

  11. The number of solutions of the equation cos^2(x+pi/6)+cos^2x-2cos(x+pi...

    Text Solution

    |

  12. (a) sin1^@>sin1(b) sin1>sin1^@(c) sin1=sin1^@

    Text Solution

    |

  13. Prove that: (sin5A-sin3A)/(cos5A+cos3A)=tanA (sinA+sin3A)/(cosA+c...

    Text Solution

    |

  14. For triangle ABC,R=5/2 and r=1. Let I be the incenter of the triangle ...

    Text Solution

    |

  15. If 5tantheta=4, then (5sintheta-3costheta)/(5sintheta+2costheta) is eq...

    Text Solution

    |

  16. Prove that (r1+r2)/(1+cosC)=2R

    Text Solution

    |

  17. Number of solutions of the equation (sqrt(3)+1)^(2x)+(sqrt(3)-1)^(2x)=...

    Text Solution

    |

  18. Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos((alpha...

    Text Solution

    |

  19. If x=(sin^3P)/cos^2P,y=cos^3P/sin^2P" and " sinP+cosP=1/2 then find th...

    Text Solution

    |

  20. Number of solution(s) of the equation (sinx)/(cos3x)+(sin3x)/(cos9x)+(...

    Text Solution

    |