Home
Class 12
MATHS
1+""^(n)C(1)cos theta+""^(n)C(2)cos 2the...

`1+""^(n)C_(1)cos theta+""^(n)C_(2)cos 2theta +…+""^(n)C_(n) cos n theta` equals

A

`("2 cos"(theta)/(2))^(n)"cos"(n theta)/(2)`

B

`"2 cos"^(2)(n theta)/(2)`

C

`"2 cos"^(2n)(theta)/(2)`

D

`("2 cos"^(2)(theta)/(2))^(n)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2015

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|80 Videos

  • QUESTION PAPER 2017

    WB JEE PREVIOUS YEAR PAPER|Exercise Multiple Choice Questions|75 Videos

Similar Questions

Explore conceptually related problems

1+.^(n)C_(1)costheta+.^(n)C_(2)cos2theta+...+.^(n)C_(n)cosntheta equals

The sum of the series 1+(1)/(2)""^(n)C_(1)+(1)/(3)""^(n)C_(2)+…+(1)/(n+1)""^(n)C_(n) is equal to-

Let S=(2)/(1)""^(n)C_(0)+(2^(2))/(2)""^(n)C_(1)+(2)/(3^(3))""^(n)C_(2)+…+(2^(n+1))/(n+1)""^(n)C_(n) . Then S equals-

Let n ge 2 be a natural number and 0 lt theta lt (pi)/(2) , Then, int ((sin^(n)theta - sin theta)^(1/n) cos theta)/(sin^(n+1) theta)d theta is equal to (where C is a constant of integration)

If theta = pi/(2^(n) + 1), "show that",2^(n) cos theta cos 2 theta cos2^(2) theta cos2^(3) theta.... cos2^(n-1) theta = 1.

Prove that, (2 cos theta - 1)(2 cos 2 theta-1)(2 cos2^(2) theta-1)...(2 cos 2^(n-1) theta-1) = (2 cos 2^(n) theta + 1)/(2 cos theta + 1)

If (1+x)^(n)=1+""^(n)C_(1)x+""^(n)C_(2)x^(2)+….+""^(n)C_(n) x^(n) show that, n*2^(n-1)=""^(n)C_(1)+2*""^(n)C_(2)+….. +n*""^(n)C_(n) .

If m^2+m^('2)+2mn'cos theta =1 n^2+n^('2)+2"nn"' cos theta=1 and mn +m'n'+(mn'+m'n)cos theta=0 then show that m^2+n^2=m^('2) +n^('2) =cosec^2 theta .

If (2lerlen) , then ""^(n)C_(r)+2.""^(n)C_(r+1)+""^(n)C_(r+2) is equal to

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2016-MULTIPLE CHOICE QUESTIONS
  1. For +ve integer n, n^(3)+2n is always divisible by

    Text Solution

    |

  2. The coefficient of x^17in the expansion of(x-1)(x-2)(x-3)….(x-18) is

    Text Solution

    |

  3. 1+""^(n)C(1)cos theta+""^(n)C(2)cos 2theta +…+""^(n)C(n) cos n theta e...

    Text Solution

    |

  4. If x, y and z be greater than 1, then the value of |(1,log(x)y,log(x)z...

    Text Solution

    |

  5. Let A is a 3xx3 matrix and B is its adjoint matrix. If |B|=64, then |A...

    Text Solution

    |

  6. Let (("cos"(pi)/(4),-"sin"(pi)/(4)),("sin"(pi)/(4),"cos"(pi)/(4))) and...

    Text Solution

    |

  7. Let R be a relation defined on the set Z of all integers and xRy when ...

    Text Solution

    |

  8. If A={3^(n)-2n-1:n in N} and B={4(n-1):n in N}, then

    Text Solution

    |

  9. If the function f : R to R is defined by f(x)=(x^(2)+1)^(35)AA x in R,...

    Text Solution

    |

  10. Standard Deviation of n observations a(1), a(2), a(3),….a(n) is sigma....

    Text Solution

    |

  11. Let A and B be two events such that P(A nn B)=(1)/(6),P(A uu B)=(31)/(...

    Text Solution

    |

  12. The value of cos 15^(@)cos 7(1^(@))/(2)sin 7(1^(@))/(2) is

    Text Solution

    |

  13. The smallest positive root of the equation tan x-x=0 lies in

    Text Solution

    |

  14. If in a triangle ABC, AD, BE and CF are the altitudes and R is the cir...

    Text Solution

    |

  15. The points (-a,-b),(a,b),(0,0) and (a^(2),ab), a ne 0, b ne 0 are alwa...

    Text Solution

    |

  16. The line AB cuts off intercepts 2a from the axes. From any point. P on...

    Text Solution

    |

  17. x+8y-22=0, 5x+2y-34=0, 2x-3y+13=0 are the three sides of a triangle. T...

    Text Solution

    |

  18. The line through the points (a, b) and (-a, -b) passes through the poi...

    Text Solution

    |

  19. The locus of the point of intersection of the straight lines (x)/(a)+(...

    Text Solution

    |

  20. The equation of a line parallel to the line 3x+4y=0 and touching the c...

    Text Solution

    |