Home
Class 12
MATHS
If z = (3+isintheta)/(4-icostheta) is pu...

If z = `(3+isintheta)/(4-icostheta)` is purely real and `theta in (pi/2,pi)` ,then `arg(sintheta + i costheta)` is -

A

`pi-tan^(-1)((4)/(3))`

B

`-tan^(-1)(3/4)`

C

`pi-tan^(-1)(3/4)`

D

`tan^(-1)(4/3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • JEE (MAIN) 2020 QUESTION PAPER MATHEMATICS (8TH JAN - MORNING)

    MCGROW HILL PUBLICATION|Exercise QUESTIONS|25 Videos

  • JEE (Main) 2020 QUESTION PAPER (8TH JAN-AFTERNOON)

    MCGROW HILL PUBLICATION|Exercise Multiple Choice Questions|25 Videos

Similar Questions

Explore conceptually related problems

If (3+2i sintheta)/(1-2i sintheta) is a real number and 0lt theta lt 2pi , then theta is a. pi \ b. pi/2 \ c. pi/3 \ d. pi/6

If z is purely real; then arg(z)=0 or pi

Find real theta in (-pi,pi) so that (3+2isintheta)/(1-2isintheta) is purely real .

Prove that sintheta (1 + Costheta) is the greatest at theta=pi/3

Which of the following is true for z=(3+2i sin theta)(1-2sin theta)wherei=sqrt(-1)?( a) z is purely real for theta=n pi+-(pi)/(3),n in Z (b)z is purely imaginary for theta=n pi+-(pi)/(2),n in Z(c)z is purely real for theta=n pi,n in Z(d) none of these

If I=[(1 ,0),( 0, 1)] , J=[(0, 1),(-1 ,0)] and B=[(costheta,sintheta),(-sintheta,costheta)] , then B equals a) Icostheta+Jsintheta (b) Isintheta+Jcostheta (c) Icostheta-Jsintheta (d) Icostheta+Jsintheta

Prove that: sqrt((1-sintheta)/(1+sintheta))= sec theta- tan theta when (-pi/2) < theta < pi/2 and -sec theta+tan theta when pi/2< theta< (3pi)/2

MCGROW HILL PUBLICATION-JEE (MAIN) 2020 QUESTION PAPER (7TH JAN - AFTERNOON) -Multiple Choice Question
  1. Let 4alpha int(-1)^2 e^(-alpha|x|) dx = 5, then alpha =

    Text Solution

    |

  2. If the sum of the first 40 terms of the series, 3+4+8+9+13+14+18+19+ ....

    Text Solution

    |

  3. If z = (3+isintheta)/(4-icostheta) is purely real and theta in (pi/2,p...

    Text Solution

    |

  4. Let A=[a(ij)] and B=[b(ij)] be two 3xx3 real matrices such that b(ij)=...

    Text Solution

    |

  5. Let f(x) is a five degree polynomial which has critical points x = pm1...

    Text Solution

    |

  6. The number of ordered pairs (r, k) for which 6(""^(35)C(r))=(k^(2)-3)(...

    Text Solution

    |

  7. Let a(1),a(2),a(3),... be a G P such that a(1)lt 0,a(1)+a(2)=4 and a(3...

    Text Solution

    |

  8. Let a, b and c be three unit vectors such that a+b+c=0. If lamda=a*b+b...

    Text Solution

    |

  9. Let y=y(x) be the solution curve of the differential equation (y^(2)-x...

    Text Solution

    |

  10. If theta(1) and theta(2) be respectively the smallest and the largest ...

    Text Solution

    |

  11. Let alpha and beta be the roots of the equation x^(2)-x-1=0 .If p(k)=(...

    Text Solution

    |

  12. The area (in sq. units) of the region {(x,y)inR^(2)l4x^(2)leyle8x+12} ...

    Text Solution

    |

  13. The value of c in the Lagrange's mean value theorem for the function f...

    Text Solution

    |

  14. if y sqrt(1-x^2) = k - x sqrt(1-y^2) and y(1/2) = -1/4, then (dy)/(dx...

    Text Solution

    |

  15. Let the tangents drawn from the origin to the circle, x^(2)+y^(2)-8x-4...

    Text Solution

    |

  16. If system of equation x + y + z = 6 x + 2y + 3z = 10 3x + 2y + l...

    Text Solution

    |

  17. If Q(5/3,7/3,17,3) is foot of perpendicular drawn from P(1, 0, 3) on a...

    Text Solution

    |

  18. If the function f(x) = {((sin^(2)ax)/(x^(2))","," when "x != 0),(" ...

    Text Solution

    |

  19. If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y...

    Text Solution

    |

  20. Let X = {x : 1 le x le 50, x in N} A = {x: x is multiple of 2} B = {...

    Text Solution

    |