Home
Class 12
MATHS
If ABCD is a cyclic quadrilateral then t...

If ABCD is a cyclic quadrilateral then the value of cosA+cosB+cos C+cos D is

Text Solution

Verified by Experts

We know that the opposite angles of a cyclic quadrilateral are supplementary, i.e., `A+C=pi" and " B+ D=pi`. Therefore,
`A=pi-C" and " B=pi-D`
`rArr cosA=cos(pi-C)=-cosD`
and `cosB=cos(pi-D)=-cosD`
`:. cosA+cosB+cosC+cos D`
`=-cosC-cosD+cosC+cosD=0`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise example|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.1|8 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

If A, B, C, D are the four angle taken in order of a cyclic quadrilateral, prove that (iii) cos A + cos B + cos C + cos D = 0

If angle A = 100^@ of a cyclic quadrilateral ABCD, then the value of angle C is _____

ABCD is a cyclic quadrilateral. If the ratio of three consecutive angles of this quadrilateral be 5 : 6 : 7, the the ratio of the 1 st and 4th angle is

ABCD is a cyclic quadrilateral and O is the centre of the circle and AB is the diameter. If AB||DC and angleBAC = 25^@ then angleDAC =

A, B, C, D are the four angles, taken in order of a cyclic quadrilateral. Prove that, cot A + cot B + cot C + cot D = 0

ABCD is a cyclic quadrilateral. If angleA = 100^@ then angleC =

If A,B,C,D are the successive angles of a cyclic quadrilateral, then- (iii) cot A - cot B + cot C - cot D =

ABCD is a cyclic quadrilateral. If angleA = 80^@ , then angleC =

ABCD is a cyclic quadrilateral. If AB = DC, then prove that AC= BD.

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. If ABCD is a cyclic quadrilateral then the value of cosA+cosB+cos C+co...

    Text Solution

    |

  2. The circular wire of diameter 10 cm is cut and placed along the circum...

    Text Solution

    |

  3. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

    Text Solution

    |

  5. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  6. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  7. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

    Text Solution

    |

  9. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  10. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

    Text Solution

    |

  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

    Text Solution

    |

  12. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  13. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  14. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  15. Simplify :cos(x-(pi)/(2)).tan((3pi)/(2)+x)

    Text Solution

    |

  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

    Text Solution

    |

  17. Which of the following is true ?

    Text Solution

    |

  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

    Text Solution

    |

  19. Which of the following is greatest ?

    Text Solution

    |

  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

    Text Solution

    |

  21. Which of the following is not correct ?

    Text Solution

    |