Question

The least value of $co{s}^2\theta -6sin\theta cos\theta +3si{n}^2\theta +2$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$co{s}^2\theta -6sin\theta cos\theta +3si{n}^2\theta +2=(co{s}^2\theta +si{n}^2\theta )-6sin\theta cos\theta +2si{n}^2\theta +2=2si{n}^2\theta -3sin2\theta +3=1-cos2\theta -3sin2\theta +3=4-(cos2\theta +3sin2\theta )\therefore Leastvalue=c-\sqrt{a^2+b^2}=4-\sqrt{10}$