Home
Class 12
MATHS
The maximum value of (cosalpha(1))(cos a...

The maximum value of `(cosalpha_(1))(cos alpha_(2))...(cosalpha_(n)),`
under the restrictions `0lealpha_(1),alpha_(2)...,alpha_(n)le(pi)/(2)` and
`(cotalpha_(1))(cotalpha_(2))......(cotalpha_(n))=1` is

A

`(1)/(2^(n//2))`

B

`(1)/(2^(n))`

C

`(1)/(2n)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise MAXIMA AND MINIMA EXERCISE 6|2 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

If 1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are n, nth roots of unity, then (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))...(1-alpha_(n-1)) equals to

The value of lim_(xto4)((cos alpha)^(x)-(sinalpha)^(x)-cos 2alpha)/(x-4), alpha epsilon(0,(pi)/2) is

Sum the series: sqrt(1+cos alpha)+sqrt(1+cos 2alpha)+sqrt(1+cos 3alpha) +.......to n terms, where 0ltalphaltpi

If (sin alpha)^(x)+(cos alpha)^(x) ge 1,0 lt a lt (pi)/(2) then

integrate int (cos2x-cos2alpha)/(cosx-cosalpha) dx

If a_(1),a_(2),".....", are in HP and f_(k)=sum_(r=1)^(n)a_(r)-a_(k) , then 2^(alpha_(1)),2^(alpha_(2)),2^(alpha_(3))2^(alpha_(4)),"....." are in {" where " alpha_(1)=(a_(1))/(f_(1)),alpha_(2)=(a_(2))/(f_(2)),alpha_(3)=(a_(3))/(f_(3)),"....."} .

If t a nbeta=(n sinalphacosalpha)/(1-n sin^2alpha) , show that tan(alpha-beta)=(1-n)t a nalphadot

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  2. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  3. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  4. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  5. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

  6. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  7. If f(x) is a cubic polynomil which has local maximum at x=-1 . If f(2)...

    Text Solution

    |

  8. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  9. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  10. Find the value of 71 - (-25) + 37 - 18 + (-11)

    Text Solution

    |

  11. Find the value of 1^2 + 2^2 + 3^2+.......+10^2

    Text Solution

    |

  12. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

    Text Solution

    |

  13. Find the value of 2 + (-11/9)

    Text Solution

    |

  14. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  15. Evaluate int(x+cos x) dx.

    Text Solution

    |

  16. The maximum value of the expression (1)/(sin ^(2) theta + 3 sin thet...

    Text Solution

    |

  17. The maximum value of the function f(x)=2x^3-15 x^2+36 x-48 on the set ...

    Text Solution

    |

  18. A wire of length 2 units is cut into two parts which are bent respecti...

    Text Solution

    |

  19. If x =-1 and x=2 ar extreme points of f(x) =alpha log|x|+betax^(2)+x ,...

    Text Solution

    |

  20. Let a , b in R be such that the function f given byf(X) = ln |x|+bx^(2...

    Text Solution

    |