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The minimum value of f(x)-sin^(4)x+cos^(...

The minimum value of `f(x)-sin^(4)x+cos^(4)x,0lexle(pi)/(2)` is

A

`1/(2sqrt(2))`

B

`1/4`

C

`(-1)/2`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `f(x)=sin^(4)x+cos^(4)x`
`=(sin^(2)x+cos^(2)x)^(2)-2sin^(2)xcos^(2)x`
`impliesf(x)=1-1/2 sin^(2)2x`
Also `0lesin^(2)2x le 1`
`:. `Minimum value of `f(x)=1-1/2=1/2`
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