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Find the maximum and minimum values of `cos^2theta-6s inthetacostheta+3sin^2theta+2.`

Text Solution

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`cos^(2)theta-6sintheta cos theta+3sin^(2)theta+2`
`=(1+cos 2 theta)/(2)-3sin2 theta+((1-cos 2 theta))/(2)+2`
`=4-cos 2 theta-3 sin 2 theta`
Now, `-cos 2 theta-3sin 2 theta in [-sqrt(10),sqrt(10)]`
`rArr 4-cos 2 theta-3 sin 2 theta in[4-sqrt(10),4+sqrt(10))`
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