Question

Given, `f_n(x) = 1/n(sin^nx + cos^nx)` for n = 1, 2, 3, ....... Then the value of 24(f₄(x) – f₆(x)) is equal to ______.

Options

• 2.00

• 3.00

• 4.00

• 5.00

Answer 1

Given, `f_n(x) = 1/n(sin^nx + cos^nx)` for n = 1, 2, 3, ....... Then the value of 24(f₄(x) – f₆(x)) is equal to 2.00.

Explanation:

f₄(x) – f₆(x) = `1/4(sin^4x + cos^4x) - 1/6(sin^6x + cos^6x)`

= `1/4(1 - 2sin^2xcos^2x) - 1/6(1 - 3sin^2xcos^2x)`

= `1/4 - 1/6`

= `1/12`

⇒ 24(f₄(x) – f₆(x)) = 2