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Range of f(theta)=cos^2theta(cos^2theta+...

Range of `f(theta)=cos^2theta(cos^2theta+1)+3sin^2theta` is

A

`[2,9//4]`

B

`[2,3]`

C

`[3//4,17//4]`

D

`[4,17//4]`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(theta)=cos^2theta(cos^2theta+1)+2sin^2theta`
`=cos^4theta+cos^2theta+sin^2theta+sin^2theta`
`=cos^4theta+1+1-cos^2theta`
`=(cos^2theta-1/2)^2+2-1/4`
`=(cos^2theta-1/2)^2+7/4`
`f_("min")=7/4`
`f_("max")=1/4+7/4=2`
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