Home
Class 12
MATHS
Let (1+isin alpha)/(1-2i sin alpha) is p...

Let `(1+isin alpha)/(1-2i sin alpha)` is purely imaginary and `(1+i cos beta)/(1-2i cos beta)` is purely real , where `alpha,beta in [pi,2pi] and z=sin 2alpha +icos2beta` , then `sum(iz+1/(ibarz))` is equal to

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematic section B|10 Videos

  • JEE MAIN 2023

    JEE MAINS PREVIOUS YEAR|Exercise Question|435 Videos

Similar Questions

Explore conceptually related problems

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) where alpha,beta in[0,(pi)/(2)], then tan(alpha+2 beta)tan(2 alpha+beta) is equal to

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

If cos alpha+cos beta=0=sin alpha+sin beta, then cos2 alpha+cos2 beta is equal to

If cos alpha=(2cos beta-1)/(2-cos beta) then tan((alpha)/(2))*cot((beta)/(2)) has the equal to [where alpha,beta in(0,pi)]

Let (sqrt(2)sin alpha)/sqrt(1+cos 2alpha)=1/7 and sqrt((1-cos2 beta)/2)=1/sqrt(10) where alpha,beta in (0,pi/2) . Then tan(alpha+2beta) is equal to

If sin (alpha - beta) =1/2 and cos (alpha + beta) =1/2, where alpha and beta are positive acute angles, then alpha and beta are

(sinalpha cos beta+cos alpha sin beta)^2+(cos alpha cos beta-sin alpha sin beta)^2=1

JEE MAINS PREVIOUS YEAR-JEE MAIN 2022-Question
  1. A=[(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma ,alpha+gamm...

    Text Solution

    |

  2. Let n^(th)term of any sequence is given Tn=(-1^3+2^3-3^3+4^3+. . .+(2n...

    Text Solution

    |

  3. Let (1+isin alpha)/(1-2i sin alpha) is purely imaginary and (1+i cos b...

    Text Solution

    |

  4. The remainder when 7^(2022)+3^(2022) is divisible by 5 is

    Text Solution

    |

  5. The sum of all the values of x satisfying cos^(-1)x-2sin^(-1)x=cos^(-1...

    Text Solution

    |

  6. f(x)=int0^x e^(x-t)f'(t)dt+e^x(x^2-x+1). Find maximum value of f(x).

    Text Solution

    |

  7. If y=cos^(-1)(x^2-4x+2)/(x^2+3) , then domain is :

    Text Solution

    |

  8. If xdy=(sqrt(x^2+y^2)+y)dx and y(1)=0, then y(2) equals:

    Text Solution

    |

  9. If a(n+2)=2/a(n+1)+an,a1=1,a2=2 , and ((a1+1/a2)/a3).((a2+1/a3)/a4)......

    Text Solution

    |

  10. Let z1 in C,|z1-3|=1/2,z2 in C, |z2+|z2-1||=|z2-|z2+1||, then least va...

    Text Solution

    |

  11. If A=[[0,1,0],[1,0,0],[0,0,1]] and B0=2A^(98)+A^(49),Bn=adj(B(n-1)), t...

    Text Solution

    |

  12. Tangent at two points P and Q on parabola y^2=2x-3 meet at R(0,1) , th...

    Text Solution

    |

  13. Let hyperbola H : x^2-y^2=1 and ellipse E : x^2/a^2+y^2/b^2=1 and ecce...

    Text Solution

    |

  14. A(cos t , sin t), B(sin t ,-cos t) and C(a,b) form an equilateral tria...

    Text Solution

    |

  15. A password is to be made of 6 to 8 digits from either of the sets A,B,...

    Text Solution

    |

  16. The solution of differential equation sin^2(2x) dy/dx+(8sin^2(2x)+4 si...

    Text Solution

    |

  17. Let f(x)=(5x^2)/2 +alpha/x^5, (x gt 0) and minimum value of f(x) is 14...

    Text Solution

    |

  18. If (p^(**)q) odot (p odot ~q) is tautology then ordered pair (odot ,^(...

    Text Solution

    |

  19. Let x^2+y^2-x+2y=11/4 is a circle with RQ and centre C. If P is any po...

    Text Solution

    |

  20. Let A relation R on number defined by xRy hArr 3x+alpha y is multiple ...

    Text Solution

    |