Home
Class 12
MATHS
Let fk(x)=1/k(sin^k x+cos^k x) Then f4(x...

Let `f_k(x)=1/k(sin^k x+cos^k x)` Then `f_4(x)-f_6(x)` =

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 PUBLICATION|Exercise Archives JEE Advanced single correct answer type|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Archives JEE Advanced Multiple correct answers type|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Numerical Value Type|11 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

Let f_(k) ""=(1)/(k) ( sin ^(k) x + cos^(k)x), where x in RR and k gt 1 then f_(4) (x)- f_(6)(x) equals -

If f(x)=sin^6x+cos^6x , then range of f(x) is

Let f(x)=sin^(4)x-cos^(4)x int_(0)^((pi)/(2))f(x)dx =

Let f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x) for some real number k. Determine(a) all real numbers k for which f(x) is constant for all values of x.

If f(x) =1/2 ( sin x+ cos x) + ce ^(-x), then the vlaue of [f ' (x)+ f(x) ] is=

Let f(x)=e^(cos^-1sin(x+pi/3)) , then

Let f(x)=sin^(4)x-cos^(4)xandg(x)=1-2sin^(2)xcos^(2)x . int_(0)^((pi)/(4))(f(x))/(g(x))dx =

Let f(x) = (ax+b) cos x+ (cx+ d) sin x and f' (x) = x cos x be an identity in x then

Let f(x)=sin^(4)x-cos^(4)xandg(x)=1-2sin^(2)xcos^(2)x . intg(x)dx =

If the function f(x)=(a sin x+2 cos x)/(sin x + cos x) is strictly increasing for all values of x, then a gt k , find k.