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)`

Question

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(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`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29