Home
Class 11
MATHS
If A ,\ B ,\ C ,\ D be the angles of a c...

If `A ,\ B ,\ C ,\ D` be the angles of a cyclic quadrilateral, taken in order, prove that: `cos(180^0-A)+cos(180^0+B)+cos(180^0+C)-sin(90^0+D)=0`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|120 Videos

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

Similar Questions

Explore conceptually related problems

If A ,\ B ,\ C ,\ D are angles of a cyclic quadrilateral, prove that cos A+cos B+cos C+cos D=0.

If A ,B ,C ,D are angles of a cyclic quadrilateral, then prove that cos A+cos B+cos C+cos D=0

If A,B,C and D are the angles of cyclic quadrilateral, prove that: i) cosA + cosB+cosC+cosD = 0 ii) cos(180^(@)-A)+cos(180^(@)+B)+cos(180^(@)+C)-sin(90^(@)+D) = 0

If A,B,C,D are the angles of a quadrilateral, prove that "cos"1/2(A+B)+"cos"1/2(C+D)=0 .

In a DeltaA B C prove that cos(A+B)+cos C=0.

Prove that the sum of opposite pair of angles of a cyclic quadrilateral is 180^@

If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A+B)=cos(C+D)

If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A+B)=cos(C+D)

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

In a cyclic quadrilateral A B C D , if /_A-\ /_C=60^0, prove that the smaller of two is 60^0

RD SHARMA ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. In a DeltaA B C prove that cos ((A+B)/2)=sin (C/2).

    Text Solution

    |

  2. In a "DeltaA B C prove that tan(("A"+"B")/2)=cot("C"/2)

    Text Solution

    |

  3. If A ,\ B ,\ C ,\ D be the angles of a cyclic quadrilateral, taken in ...

    Text Solution

    |

  4. Find x from the following equation: cos e c(90^0+theta)+x costhetacot(...

    Text Solution

    |

  5. Find x from the following equation: xcot(90^0+theta)+tan(90^0+theta)si...

    Text Solution

    |

  6. Prove that: t a n 720^0-cos 270^0-sin 150^0cos 120^0=1/4

    Text Solution

    |

  7. Prove that: sin 780^0sin 480^0+cos 120^0sin 150^0=1/2

    Text Solution

    |

  8. Prove that: sin780^0sin 120^0+cos 240^0sin390^0=1/2

    Text Solution

    |

  9. Prove that: sin600^0cos 390^0+cos 480^0sin 150^0=-1

    Text Solution

    |

  10. Prove that : tan 225^@ cot 405^@+ tan 765^@ cot 675^@=0

    Text Solution

    |

  11. Write the maximum and minimum values of cos(cosx)

    Text Solution

    |

  12. Write the maximum and minimum values of sinx dot

    Text Solution

    |

  13. Write the maximum value of sin(cosx)dot

    Text Solution

    |

  14. If sin x=cos^2x ,\ then write the value of cos^2x\ (1+cos^2x)dot

    Text Solution

    |

  15. If sin x+cosec\ x=2, then write the value of sin^n x+cos e c^n xdot

    Text Solution

    |

  16. If sintheta1+sintheta2+sintheta3=3, then costheta1+costheta2+costheta3...

    Text Solution

    |

  17. Write the value of sin 10^0+sin 20^0+sin 30^0+....+sin 360^@

    Text Solution

    |

  18. A circular wire of radius 15cm is cut and bent so as to lie along the ...

    Text Solution

    |

  19. The value for 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1 is

    Text Solution

    |

  20. Write the value of cos1^0+cos2^0+cos3^0++cos 180^0dot

    Text Solution

    |