Home
Class 12
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

`1/6`

B

`1/3`

C

`1/4`

D

`1/12`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|22 Videos
  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos
  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 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

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If alpha and beta are non-zero real number such that 2(cos beta-cos al...

    Text Solution

    |

  2. Let -1/6 < theta < -pi/12 Suppose alpha1 and beta1, are the root...

    Text Solution

    |

  3. The value of sum(k=1)^(13) (1)/(sin(pi/4 + ((k-1)pi)/(6))sin(pi/4 + (k...

    Text Solution

    |

  4. Let f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for t...

    Text Solution

    |

  5. The number of all possible values of theta, where 0 lt theta lt pi, f...

    Text Solution

    |

  6. For 0 lt theta lt pi/2, the solution (s) of sum(m=1)^(6) cosec (the...

    Text Solution

    |

  7. If sin^ 4 x/2+cos^4 x/3 =1/5 then

    Text Solution

    |

  8. Let theta in (0,pi/4) and t1=(tan theta)^(tan theta), t2=(tan theta)6(...

    Text Solution

    |

  9. cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...

    Text Solution

    |

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

    Text Solution

    |

  14. If A = sin^2x + cos^4 x, then for all real x :

    Text Solution

    |

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

    Text Solution

    |

  16. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...

    Text Solution

    |

  17. A triangular park is enclosed on two sides by a fence and on the third...

    Text Solution

    |

  18. If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is

    Text Solution

    |

  19. In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...

    Text Solution

    |