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
Given, `f_(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x)`, where `x in R` and `k ge 1`
`:.f_(4)(x)-f_(6)(x)=(1)/(4)(sin^(4)x+cos^(4)x)-(1)/(6)(sin^(6)x+cos^(6)x)`
`=(1)/(4)(1-2sin^(2)x.cos^(2)x)-(1)/(6)(1-3sin^(2)x.cos^(2)x)`
`=(1)/(4)-(1)/(6)=(1)/(12)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEMS)|30 Videos

  • SETS, RELATIONS AND FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 1 (TOPICAL PROBLEMS) Domain-Range, Odd-Even and Periodic Functions|11 Videos

  • SEQUENCES AND SERIES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 31|1 Videos

  • SOLVED PAPER 2017

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MCQS|50 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

Knowledge Check

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

    A
    `1//6`
    B
    `1//3`
    C
    `1//4`
    D
    `1//12`

  • Let f_(k)(x)=1/(k)("sin"^(k)x+"cos"^(k)x) where x inRandkge1 then f_(4)(x)-f_(6)(x) equals

    A
    `1/(6)`
    B
    `1/(3)`
    C
    `1/(4)`
    D
    `1/(12)`

  • Let f_(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x) for k = 1, 2, 3……. Then for all x in R, Then values of f_(4)(x)-f_(6)(x) is equal to

    A
    `5//12`
    B
    `-1//12`
    C
    `1//2`
    D
    `1//12`

    • Similar Questions

    Explore conceptually related problems

    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

    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 :

    Home
    Profile