Home
Class 12
MATHS
If (pi)/(2) lt alpha (3pi)/(2) , the mod...

If `(pi)/(2) lt alpha (3pi)/(2) , the modulus argument form of `(1 + cos 2 alpha) + isin 2 alpha` is

A

`- 2 cos alpha {cos (alpha - pi) +isin (alpha - pi)}`

B

`2 cos alpha (cos alpha + isin alpha)`

C

`2 cos alpha {cos (-alpha) + isin (-alpha)}`

D

`- 2 cos alpha { cos (pi - alpha) + isin (pi - alpha)}`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise EXERCISE -II|126 Videos

  • CIRCLES

    AAKASH SERIES|Exercise PRACTICE EXERCISE|164 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

Similar Questions

Explore conceptually related problems

I : If (cos alpha )/(a)=(sin alpha )/(b) then a cos 2 alpha + b cos 2 alpha =a II : If (sin alpha )/(a) =(cos alpha )/(b) then a sin 2 alpha + b cos 2 alpha = a

If 0 lt alpha lt (pi)/(6) then alpha(cosec alpha) is

If -(pi)/2 lt alpha lt (pi)/2 then prove that tan^(-1)((3sin 2 alpha)/(5+3 cos alpha))+tan^(-1)((tan alpha)/4)=

If the product of the intercepts made by the straight line x tan alpha + y sec alpha =1, (0 le alpha le (pi)/2) , on the co-ordinates axes is equal to sin alpha , find alpha .

If sin alpha =(3)/(5) , where (pi)/(2) lt alpha lt pi , evaluate cos 3 alpha and tan 2 alpha .

If the product of the intercepts make by the straight line xtan alpha+y sec alpha=1, (0 le alpha lt (pi)/2) , on the co-ordinates axes is equal to sin alpha, find alpha .

If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cot alpha)-cot^(-1)(tan alpha)+sin^(-1)(sin alpha)+cos^(-1)(cos alpha) is equal to

AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
  1. The mod-amplitude form of -sqrt3 - i

    Text Solution

    |

  2. The mod-amplitude form of sin theta + icos theta is

    Text Solution

    |

  3. If (pi)/(2) lt alpha (3pi)/(2) , the modulus argument form of (1 + cos...

    Text Solution

    |

  4. If (pi)/(5) and (pi)/(3) are respectively the arguments of barz(1) and...

    Text Solution

    |

  5. If Arg (3z-2i) = pi//2 then the locus of z = x +iy is

    Text Solution

    |

  6. The argument of ((1 - isqrt3))/((1+isqrt3)) is equal to

    Text Solution

    |

  7. Given |z| = 14 and amp z = (7pi)/(6) , then z is =

    Text Solution

    |

  8. If (sqrt3 + i) = (a + ib) (c + id) then tan^(-1) (b)/(a) + tan^(-1) (d...

    Text Solution

    |

  9. Let z,w be complex number such that barz+ibarw=0 and arg zw =pi . Then...

    Text Solution

    |

  10. If Arg ((z+1)/(z-1))=pi/6 then the locus of z = x + iy is

    Text Solution

    |

  11. If |z| = 1 and arg [z^(2) + barz] = x arg z then x

    Text Solution

    |

  12. If z = x + iy and if the point P in the Argand plane represents z , th...

    Text Solution

    |

  13. If |z-3+i| = 4 then the locus of z = x +iy is

    Text Solution

    |

  14. If |(z-1)/(z-3)| = 2 then the locus of z = x +iy is

    Text Solution

    |

  15. The locus of the point z = x +iy satisfying the equation |(z-1)/(z+1)|...

    Text Solution

    |

  16. The equation of the locus of 2 such that |(z-i)/(z+i)|=2, where z = x ...

    Text Solution

    |

  17. The locus of the point z in the argrand plane for which |z+1|^2+|z-1|^...

    Text Solution

    |

  18. If |z+i|^2-|z-i|^2=3 then the locus of z is

    Text Solution

    |

  19. The points representing the complex numbers z for which |z+4|^2-|z-4|^...

    Text Solution

    |

  20. If (2z(1))/(3z(2)) is purely , an imaginary number , then |(z(1) - z(2...

    Text Solution

    |