Home
Class 12
MATHS
Let fK(x)""=1/k(s in^k x+cos^k x) where ...

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)`

A

`1/6`

B

`1/3`

C

`1/4`

D

`1/12`

Text Solution

Verified by Experts

The correct Answer is:
D
`f_4(x) -f_6(x) =1/4(sin^4x+cos^4x)-1/6(sin^6+cos^6x)`
`=(3(sin^4x+cos^4x)-2(sin^6+cos^6x))/12`
`=(3(1-2sin^2cos^2x)-2(1-3sin^2xcos^2x))/12`
`1/12`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|2 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Numerical)|11 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

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

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)

Let f(x)=int e^(x^(2))(x-2)(x-3)(x-4)dx then f increases on (k,k+1) then k is

If f(x)=(cos(sinx)-cosx)/x^4 is continuous over the domain and f(0)=1/k , then k=?