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Find the minimum value of 2sin^2theta+3c...

Find the minimum value of `2sin^2theta+3cos^2theta`

Text Solution

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`f(theta) = 2sin^2theta+3cos^2theta`
`= 2(cos^2theta+sin^2theta)+cos^2theta`
`=2+cos^2theta`
`=2+1/2(1+cos2theta)`
`=2+1/2+1/2cos2theta`
`f(theta)=5/2+1/2cos2theta`
`f(theta)` will be minimum when `cos2theta = -1`
`:f(theta)_min = 5/2-1/2 = 2 `
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