Home
Class 11
MATHS
Let alpha, beta" such that "pi lt alpha-...

Let `alpha, beta" such that "pi lt alpha-beta lt 3pi." If sin "alpha+sin beta=-21//65 cos alpha+cos beta=-27//65`, then find the value of `cos ""(alpha-beta)/(2)`.

Text Solution

Verified by Experts

The correct Answer is:
`- (3)/(sqrt(130))`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY

    FULL MARKS|Exercise Exercise 3.1|12 Videos

  • TRIGONOMETRY

    FULL MARKS|Exercise Exercise 3.2|11 Videos

  • TRIGONOMETRY

    FULL MARKS|Exercise Exercise 3.12|20 Videos

  • SOLVED PAPER 10

    FULL MARKS|Exercise PART-IV|8 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY

    FULL MARKS|Exercise Additional Questions Solved|19 Videos

Similar Questions

Explore conceptually related problems

Let alpha , beta be such pi lt alpha- beta lt 3 pi if sin alpha + sin beta = (-21)/(65) , and cos alpha Cos beta = (-27)/(65) then the value of cos ( alpha - beta)/(2) is

If cos alpha + cos beta = 1//2 and sin alpha+ sin beta = 1//3 , then

If alpha+ beta=-7 and alpha beta=10 then find the value of alpha-beta=__ .

sin alpha+sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) the value of sin(alpha+beta)

If sin^4alpha+cos^4beta+2=4sinalphacosbeta,0lt=alpha,betalt=pi/2 then find the value of (sinalpha+cosbeta)dot

If alpha , beta in (0,pi/2), sin alpha =4/5 and cos ( alpha + beta) = ( -12)/(13) then sin beta is equal to

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

If cos alpha + cos beta =0 = sin alpha + sin beta , then cos 2 alpha + cos 2 beta is equal to

If alpha and beta are roots of the equatioin a cos theta + b sin theta = c , then find the value of tan (alpha + beta).

FULL MARKS-TRIGONOMETRY-Additional Questions Solved
  1. A horse is tied to a post by a rope. If the horse moves along a circul...

    Text Solution

    |

  2. A circular wire of radius 3 cm is out bent so as to lie along the circ...

    Text Solution

    |

  3. Let alpha, beta" such that "pi lt alpha-beta lt 3pi." If sin "alpha+si...

    Text Solution

    |

  4. Prove that sin 600^(@)* tan (-690^(@))+sec 840^(@)*cot(-945^(@))=3/2

    Text Solution

    |

  5. Prove that sin (270^(@)-theta) sin (90^(@)-theta)-cos(270^(@)-theta) c...

    Text Solution

    |

  6. Prove that cos 24^(@)+cos 55^(@)+cos 125^(@)+cos 204^(@)+cos 300^(@)=1...

    Text Solution

    |

  7. Prove that cos^(2)""pi/8+cos^(2) ""(3pi)/(8)+cos^(2)""(5pi)/(8)+cos^(2...

    Text Solution

    |

  8. Prove that [1+cot alpha-sec(alpha+pi/2)] [1+cot alpha+sec (alpha+pi/2)...

    Text Solution

    |

  9. Write the general form for tantheta

    Text Solution

    |

  10. Simplify (cos(90^@+theta)sec (-theta)tan(180^(@)-theta))/(sec(360^(@)-...

    Text Solution

    |

  11. Find x from the equation cosec (90^(@)+A)+x cos A cot (90^(@)+A)=sin(9...

    Text Solution

    |

  12. Prove that sin (A+B) sin (A-B)=cos^(2) B-cos^(2) A

    Text Solution

    |

  13. Prove that (i) sin A+sin (120^(@)+A)+sin(240^(@)+A)=0 (ii) cos A+c...

    Text Solution

    |

  14. If tan A=5/6, tan B=1/11," show that A+B=45"^(@).

    Text Solution

    |

  15. If A+B=45^(@)," show that "(1+tan A) (1+tan B)=2 and hence deduce the ...

    Text Solution

    |

  16. If tanalpha=1/3,tanbeta=1/7,show that 2alpha +beta=pi/4

    Text Solution

    |

  17. If 2 cos theta=x+1/x then prove that cos 2 theta=1/2 (x^(2)+1/x^(2))

    Text Solution

    |

  18. Prove that cos 20^(@) cos 40^(@) cos 80^(@)=1/8

    Text Solution

    |

  19. Show that 4 sin A sin (60^(@)+A). Sin (60^(@)-A) =sin 3A

    Text Solution

    |

  20. Prove that cos 20^(@) cos 40^(@) cos 80^(@)=1/8

    Text Solution

    |