The least value of `[cos^2 theta-6 sin theta. cos theta+3 sin^2 theta + 2]` is

Options

A. `4+sqrt10`
B. `4-sqrt10`
C. 0
D. none of these

Answer

B

Explanation

We have,
`y=cos^(2)theta-6sinthetacostheta+3sin^(2)theta+2`
`impliesy=((1+cos2 theta)/(2))-3sin2 theta+3((1-cos2 theta)/(2))+2`
`impliesy=-cos2 theta-3sin2theta+4`
Now, `-sqrt10le-cos2 theta-3sin2 thetale sqrt10"for all"theta`
`implies-4sqrt10leyle4+sqrt10`
Hence, the least value of y is `4-sqrt10.`