Home
Class 12
MATHS
If A,B,C,D are the angles of a cyclic qu...

If A,B,C,D are the angles of a cyclic quadrilateral then ` cos A + cos B+ cos C + cos D=`

Text Solution

Verified by Experts

The correct Answer is:
`cos A+ cos B + cos C+ cos D =0`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIONS, TRANSFORMATIONS

    SRISIRI PUBLICATION|Exercise VSAQ|51 Videos

  • TRIGONOMETRIC EQUATIONS

    SRISIRI PUBLICATION|Exercise SPQ|8 Videos

Similar Questions

Explore conceptually related problems

I: If A,B,C,D are angles of a cyclic quadrilateral then cos A + cos B + cos C + cos D=0 II : If A,B,C,D are the angles of a quadrilateral then cos""(A+B)/(2) + cos""(C+D)/(2) =0

If A,B,C,D are the angles of a cyclic quadrilateral then sinA+sinB=

If A, B, C, D are angles of a cyclic quadrilateral then P.T sin A - sin C = sin D - sin B .

If ABCD is a cyclic quadrilateral then show that i) cos A + cos B + cos C + cos D = 0 ii) sin A + sin B = sin C + sin D

If A,B,C,D are the angles of a quadrilateral then cos""((A+B)/(2))+ cos ""((C+D)/(2)) =

Assertion (A): If A, B, C are the angles of a triangle such that cos A + cos B + Cos C = 0 = sin A + sin B + sin C then cos 3A + cos 3B + cos 3C = -3 Reason (R) : If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + singamma then cos 3 alpha + cos 3 beta + cos 3 gamma = 3 cos (gamma+alpha+beta)

SRISIRI PUBLICATION-TRIGONOMETRIC RATIONS, TRANSFORMATIONS-LAQ
  1. Show that cos ^(4) alpha + 2 cos ^(2) alpha (1-(1)/(sec ^(2) alpha ))=...

    Text Solution

    |

  2. For what values of x in the first quadrant (2 tan x)/( 1- tan ^(2) x) ...

    Text Solution

    |

  3. If A,B,C,D are the angles of a cyclic quadrilateral then cos A + cos...

    Text Solution

    |

  4. Express cos^(6)A + sin^(6)A interms of sin 2A.

    Text Solution

    |

  5. Prove that sin ^(2) ((pi)/(8)+(A)/(2)) - sin ^(2) ((pi)/(8) - (A)/(2))...

    Text Solution

    |

  6. Expres sqrt3 sin 0 + cos 0 as a sine of an angle .

    Text Solution

    |

  7. Simplify tan ((pi)/(4) +A) tan ((pi)/(4)-A)

    Text Solution

    |

  8. Find the value of tan 75^(@) + cot 75^(@)

    Text Solution

    |

  9. If tan theta =(cos 11^(@) + sin 11^(@) )/( cos 11^(@)- sin 11^(@)) and...

    Text Solution

    |

  10. If sin A=(12)/(13), cos B= (3)/(5) and neither A nor B is in the first...

    Text Solution

    |

  11. If 0 lt A, B lt 90^(@), cos A= (5)/(13) and sin B =(4)/(5) then find s...

    Text Solution

    |

  12. If sin =(1)/(sqrt10), sin beta =(1)/(sqrt5) and alpha , beta are acu...

    Text Solution

    |

  13. If cos theta =(-5)/(13) and (pi)/(2) lt theta lt pi , find the value...

    Text Solution

    |

  14. If cos theta = t(0lt t lt 1) and theta does not lies in the first qua...

    Text Solution

    |

  15. If 0 lt A lt pi //4 and cos A = 4//5, then find the values of sin 2...

    Text Solution

    |

  16. If cos theta =(5)/(13) and 270 ^(@) lt theta lt 360^(@), evaluate sin ...

    Text Solution

    |

  17. If sin alpha =(3)/(5) , where (pi)/(2) lt alpha lt pi , evaluate cos ...

    Text Solution

    |

  18. If cos 0 =(-3)/(5) and pi lt 0 lt (3pi)/(2) , find the value of tan th...

    Text Solution

    |

  19. Prove that (sin theta + sin 2 theta )/(1+cos 0 + cos 2 theta )= tan th...

    Text Solution

    |

  20. If theta is not an integral multiple of (pi)/(2), prove that tan thet...

    Text Solution

    |