Question

What is the minimum value of `2sin^2theta+3cos^2theta`?

Answer 1

Let

`y=2sin^2theta+3cos^2theta`

`=>y=2sin^2theta+2cos^2theta+cos^2theta`

`=>y=2(sin^2theta+cos^2theta)+cos^2theta`

`=>y=2+cos^2theta`

So y will be minimum when `cos^2theta=0`

Hence `y_(min)=2`