Home
Class 11
MATHS
Let fk(x) = 1/k(sin^k x + cos^k x) where...

Let `f_k(x) = 1/k(sin^k x + cos^k x)` where `x in RR` and `k gt= 1.` Then `f_4(x) - f_6(x)` equals

A

`(1)/(3)`

B

`(1)/(4)`

C

`(1)/(12)`

D

`(1)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY

    MODERN PUBLICATION|Exercise Chapter Test (3)|12 Videos

  • TRIGONOMETRY

    MODERN PUBLICATION|Exercise Check your unders"tan"ding|10 Videos

  • STRAIGHT LINES

    MODERN PUBLICATION|Exercise Chapter test|12 Videos

Similar Questions

Explore conceptually related problems

Let f_K(x)""=1/k(s in^k x+cos^k x) where x in R and kgeq1 . Then f_4(x)-f_6(x) equals (1) 1/6 (2) 1/3 (3) 1/4 (4) 1/(12)

Let f_(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x) where x in R and k>=1. Then f_(4)(x)-f_(6)(x) equals

Let f_(1)(x) = x/(x+1) AA x in R^(+) , se of positive real numbers, For k ge 2 , define f_(k)(x) = f_(k-1)(f_(1)(x)) AA x in R^(+) Then f_(2020)(1/2020) is equal to

Let f (x)= sin ^(-1) x-cos ^(-1), x, then the set of values of k for which of |f (x)|=k has exactly two distinct solutions is :

If f_(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x) then f_(4)(x)-f_(6)(x)=(A)(1)/(12) (B) (5)/(12) (C) (-1)/(12) (D) -(5)/(12)

The function f(x) is defined by f(x)=cos^(4)x+K cos^(2)2x+sin^(4)x, where K is a constant.If the function f(x) is a constant function,the value of k is

Let f(x)=4x^(2)-2x+k, where k in R If both roots of tho equation f(x)=0 lie in (-1,1) then k can be equal to

MODERN PUBLICATION-TRIGONOMETRY-COMPETITION FILE
  1. If p and q are positive real numbers such that p^2+q^2=1 then find the...

    Text Solution

    |

  2. Let A and B denote the statements A : cos alpha + cos beta + cos gam...

    Text Solution

    |

  3. Let cos(alpha+beta)=(4)/(5) and let sin(alpha-beta)=(5)/(13), where 0 ...

    Text Solution

    |

  4. If A = "sin"^(2)x + cos^(4)x then for all realx :

    Text Solution

    |

  5. The possible values of theta in (0, pi) such that sin(theta)+sin(4thet...

    Text Solution

    |

  6. The solution of the equation e^(sin x) - e^(-sin x) - 4 = 0

    Text Solution

    |

  7. If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...

    Text Solution

    |

  8. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as :

    Text Solution

    |

  9. Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...

    Text Solution

    |

  10. If 0 le x le 2pi, then the number of real values of x, which satisfy t...

    Text Solution

    |

  11. If 5(tan^2x - cos^2x)=2cos 2x + 9, then the value of cos4x is

    Text Solution

    |

  12. For a regular polygon, let r and R be the radii of the inscribed and ...

    Text Solution

    |

  13. ABCD is a trapezium such that AB and CD are parallel and BC bot CD. If...

    Text Solution

    |

  14. If the sum of all the solutions of the equation 8 cosx.(cos(pi/6+x)cos...

    Text Solution

    |

  15. The maximum values of 3 costheta+5sin(theta-(pi)/(6)) for any real val...

    Text Solution

    |

  16. cos^(2)10^(@)+cos^(2)50^(@)-cos10^(@)cos50^(@) is equal to

    Text Solution

    |

  17. Let S = { theta in [-2pi,2pi]:2 cos^(2) theta + 3 sin theta = 0}, the...

    Text Solution

    |