Home
Class 11
MATHS
The number of ordered pairs (α,β), where...

The number of ordered pairs (α,β), where α,β∈(−π,π) satisfying cos (α−β)=1 and cos(α+β)=1/e is

Text Solution

Verified by Experts

`cos(alpha-beta)=1`
`cos(alpha-beta)=cos0`
`alpha-beta=0`
`alpha=beta`
`cos(alpha+beta)=1/e`
`cos2alpha=1/e`
`alpha=beta=4`
Option D is correct.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

The number of ordered pairs ( alpha, beta ) ,where alpha, beta in (-pi, pi) satisfying cos(alpha-beta) =1 "and" cos(alpha+beta) = (1)/(sqrt2) is :

The total number of ordered pairs (x, y) satisfying |y|=cosx and y=sin^(-1)(sinx) , where x in [-2pi, 3pi] is equal to :

The number of ordered pair (x, y) satisfying the equation sin^(2) (x+y)+cos^(2) (x-y)=1 which lie on the circle x^(2)+y^(2)=pi^(2) is _________.

The number of ordered pairs (a,b) where a,b are integers satisfying the inequality min (x ^(2) +(a-b) x + (1-a-b)) gtmax (-x ^(2) +(a+b)x-(1+a+b)AA x in R, is :

Find the number of ordered pairs of (x, y) satisfying the equation y = |sinx| and y = cos^(-1)(cosx) , where x in [-π, π]

Total number of ordered pairs (x, y) satisfying |y| = cos x and y = sin^(-1) (sin x) where |x| leq3pi is equal to

The number of ordered pair (x ,\ y) satisfying correspondence C_1 is 1 b. 2 c. 3 d. 4

If x in[0,6 pi],y in[0,6 pi] then the number of ordered pair (x,y) which satisfy the equation sin^(-1)sin x+cos^(-1)cos y=(3 pi)/(2) are

The number of ordered pairs (alpha , beta ) , where alpha , beta in [0,2pi] satisfying log_(2 sec x )(beta^(2)-6beta+10)=log_(3)| cos alpha | is

The number of ordered pair(s) (x, y) of real numbers satisfying the equation 1+x^(2)+2x sin(cos^(-1)y)=0 , is :

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. D , E ,a n dF are the middle points of the sides of the triangle A B C...

    Text Solution

    |

  2. If cos(A-B)=3/5 and tan A tan B=2, then (a) cos Acos B=1/5 (b) sin A ...

    Text Solution

    |

  3. The number of ordered pairs (α,β), where α,β∈(−π,π) satisfying cos (α−...

    Text Solution

    |

  4. The base B C of A B C is fixed and the vertex A moves, satisfying the...

    Text Solution

    |

  5. For 0 < varphigeqpi/2,ifx=sum(n=0)^oocos^(2n)varphi,y=sum(n=0)^oosin^...

    Text Solution

    |

  6. In a right angled triangle, acute angle A and B satisfy tanA+tanB+tan^...

    Text Solution

    |

  7. Solve sin^2x+cos^2y=2sec^2z for x , y ,a n dzdot

    Text Solution

    |

  8. if 0ltalphaltbetaltgammaltpi/ 2,then prove that tanalpha lt (sinalpha+...

    Text Solution

    |

  9. Given b=2,c=sqrt(3),/A=30^0 , then inradius of A B C is (sqrt(3)-1)/2...

    Text Solution

    |

  10. If A,B,C are angles of a triangle, then 2sin(A/2)cosec (B/2)sin(C/2)-s...

    Text Solution

    |

  11. Solve cos^(50)x-sin^(50)x=1

    Text Solution

    |

  12. sqrt((1-sintheta)/(1+sintheta))={sectheta-tantheta , if -pi/2ltthetalt...

    Text Solution

    |

  13. If two sides of a triangle are roots of the equation x^2-7x+8=0 and th...

    Text Solution

    |

  14. Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)...(1+sec2^ntheta)=...

    Text Solution

    |

  15. If 3sinx+4cosa x=7 has at least one solution, then find the possible v...

    Text Solution

    |

  16. Prove that (cos(90^0+theta)sec(-theta)"tan"(180^0-theta))/(sec(360^0-t...

    Text Solution

    |

  17. A sector O A B O of central angle theta is constructed in a circle wit...

    Text Solution

    |

  18. Prove that: (2cos2^ntheta+1)/(2costheta+1)=(2costheta-1)(2cos2theta-1)...

    Text Solution

    |

  19. Find the number of solution of sin^2xcos^2x=1+cos^2xsin^4x in the inte...

    Text Solution

    |

  20. Prove that sin(-420^0)(c0s390^0)+cos(-660^0)(sin330^0)=-1

    Text Solution

    |