Home
Class 11
MATHS
If any quadrilateral ABCD, prove that "...

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

Text Solution

AI Generated Solution

To prove the given relations for any quadrilateral ABCD, we will follow these steps: ### Step 1: Understand the sum of angles in a quadrilateral In any quadrilateral ABCD, the sum of the interior angles is given by: \[ A + B + C + D = 2\pi \quad \text{(in radians)} \] This means that if we know any three angles, we can find the fourth angle. ...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos
  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

In equilibrium ABCD, prove thatL: i) sin(A+B)+sin(C+D)=0 ii) cos(A+D)-cos(B+C)=0

In a quadrilateral ABCD,cos A cos B+sin C sin D=

In a Quadrilateral ABCD,cos A*cos B+sin C sin D=

In any Delta ABC ,prove that (sin B)/(sin C)=(c-a cos B)/(b-a cos C)

In any Delta ABC, prove that: (sin B)/(sin C)=(c-a cos B)/(b-a cos C)

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

In any quadrilateral ABCD, show that: cosA cosB-cosC cosD="sin"A "sin"B-"sin"C "sin"D.

In any triangle ABC,prove that sin^(3)A cos(B-C)+sin^(3)B cos(C-A)+sin^(3)C cos(A-B)=3sin A sin B sin C

If A,B,C,D be the angles of a quadrilateral , what is the value of (sin(A+B))/(sin (C+D)) +(cos(C+D))/(cos (A+B))

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

RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Prove that: "sec"((3pi)/2-theta)"sec"(theta-(5pi)/2)+t a n((5pi)/2+the...

    Text Solution

    |

  2. Find the value of : sin^2(pi/(18))+sin^2(pi/9)+sin^2((7pi)/(18))+sin^2...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the value of the expression 3{sin^4((3pi)/2-theta)+sin^4(3pi+the...

    Text Solution

    |

  5. If t a n^2theta=1-a^2 , prove that sectheta+t a n^3thetacos e ctheta=...

    Text Solution

    |

  6. If acos^2theta+3acostheta sin^2theta=m and asin^3theta+3acos^2thetasin...

    Text Solution

    |

  7. If 2t a n^2alphat a n^2betat a n^2gamma+t a n^2alphat a n^2beta+t a ...

    Text Solution

    |

  8. If m^2 + m'^2 + 2mm' costheta = 1 and n^2+n'^2+2n n'costheta=1, (mn +...

    Text Solution

    |

  9. If (sin^4theta)/a+(cos^4theta)/b=1/(a+b) , prove that (sin^8theta)/...

    Text Solution

    |

  10. If (cos^4alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 prove that (i...

    Text Solution

    |

  11. If x is any non-zero real number, show that costheta' a n d ' sinthet...

    Text Solution

    |

  12. If A=cos^2theta+sin^4theta, prove that 3/4lt=Alt=1 for all values of...

    Text Solution

    |

  13. If tantheta+sectheta=e^x then costheta equals

    Text Solution

    |

  14. Prove that:sqrt((1-costheta)/(1+costheta))={cosectheta-cottheta,if 0 <...

    Text Solution

    |

  15. If sec theta=sqrt(2)a n d(3pi)/2<theta<2pi ,="" find="" the="" value="...

    Text Solution

    |

  16. Prove the following identities: sin^8theta-cos^8theta=(sin^2theta-cos^...

    Text Solution

    |

  17. Prove the following identities: cot^4theta+cot^2theta=cos e c^4theta-c...

    Text Solution

    |

  18. Prove the following identities: 2sec^2theta-sec^4theta-2cos e c^2theta...

    Text Solution

    |

  19. Prove the following identities: (sintheta+cos e ctheta)^2+(costheta+s...

    Text Solution

    |

  20. Prove the following identity: (1+cottheta-cos e ctheta)(1+t a ntheta+s...

    Text Solution

    |