Home
Class 12
MATHS
In a quadrilateral if sin(A+B)/2cos(A-B...

In a quadrilateral if `sin(A+B)/2cos(A-B)/2+sin(c+D)/2cos(c-D)/2=2,` then `cosA/2cosB/2+cosA/2cosc/2+cosA/2 cosD/2+cosB/2 cosC/2+cosB/2 cosD/2+cosC/2 cosD/2=`

Text Solution

AI Generated Solution

To solve the given problem step by step, we start with the equation provided: \[ \frac{\sin(A+B)}{2\cos(A-B)} + \frac{\sin(C+D)}{2\cos(C-D)} = 2 \] ### Step 1: Rewrite the equation ...
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|32 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment section-A (Objective Type Questions (One option is correct))|49 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - J|10 Videos

  • VECTOR ALGEBRA

    AAKASH INSTITUTE ENGLISH|Exercise SECTION-J (Aakash Challengers Questions)|5 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC, prove that: cos^4A+cos^4B+cos^4C= 3/2 + 2 cosA cosB cosC+ 1/2 cos 2A cos2B cos2C

Prove that : (a b c)/scosA/2cosB/2cosC/2=

If A+B+C=0 , Prove : cos^2 A + cos^2 B +cos^2 C=1+2cosA cosB cosC .

a(cosC-cosB)=2(b-c)cos^2A/2

In any A B C ,2(bc cosA+ ca cosB+ab cosC) =

If A+B+C=pi , prove that : cos2A+cos2B+cos2C=-1-4cosA cosB cosC

In a triangle ABC, Prove that: sin^3A+sin^3B+sin^3C = 3cosA/2 cosB/2 cosC/2 +cos (3A)/2 cos (3B)/2 cos (3C)/2

If A+B+C=2pi , prove that : cos^2B+cos^2C-sin^2A-2cosA cosB cosC=0 .

If A+B+C=pi , prove that : cosA + cosB-cosC=4cos(A/2) cos(B/2) sin(C/2) -1

If A+B+C=180^@ , then prove that cos^2 A + cos^2 B +cos^2 C=1-2cosA cosB cosC .

AAKASH INSTITUTE ENGLISH-TRIGNOMETRIC FUNCTIONS -Section - J (Akash Challengers Question)
  1. In a quadrilateral if sin(A+B)/2cos(A-B)/2+sin(c+D)/2cos(c-D)/2=2, th...

    Text Solution

    |

  2. If cos^(2009)x(1) + cos^(2009)x(2) + cos^(2009)x(3) + ………. +cos^(2009)...

    Text Solution

    |

  3. If a cos^(3) alpha+3a cos alpha sin^(2) alpha=m and a sin^(3) alpha+3a...

    Text Solution

    |

  4. If alpha satisfies 15 sin^(4)alpha + 10 cos^(4)alpha=6, then find the ...

    Text Solution

    |

  5. If A= tan27theta - tantheta and B= (sintheta)/(cos 3theta) +(sin 3thet...

    Text Solution

    |

  6. If A=sqrt(3) cot 20^(@) - 4 cos20^(@) and B= sin12^(@) sin48^(@) sin54...

    Text Solution

    |

  7. If tan alpha = 1/sqrt(x(x^2+x+1)),tan beta=sqrtx/sqrt(x^2+x+1) and ...

    Text Solution

    |

  8. The number of values of x lying in [-pi, pi] and satisfying 2sin^2the...

    Text Solution

    |

  9. The number of solutions of the equation sinx.cosx(cosx-sinx)^(2). (sin...

    Text Solution

    |

  10. The number of solutions of the equation sin^(5)theta + 1/(sintheta) = ...

    Text Solution

    |

  11. The number of solutions of x in the interval [-pi, pi] of the equation...

    Text Solution

    |

  12. The general solution of the equation tan(x+20^@)tan(x-4 0^(@))=tan(x-...

    Text Solution

    |

  13. Let x in [0,2pi] The curve y=secx tanx +2tanx - sec x and the line y=2...

    Text Solution

    |

  14. Let p (x) be a polynomial with real coefficient and p (x)=x^(2)+2x+1. ...

    Text Solution

    |

  15. Let three sets be defined as A={x|cos2x + cosx+1=0} B={x|cos2x + 3...

    Text Solution

    |

  16. The number of solutions of the equation 2^|x|=1+2|cosx| is

    Text Solution

    |

  17. If the equation 1 +sin^2 xtheta= costheta has a non-zero solution in t...

    Text Solution

    |