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

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1.	The least value of `[cos^2 theta-6 sin theta. cos theta+3 sin^2 theta + 2]` isA. `4+sqrt10`B. `4-sqrt10`C. 0D. none of these
Answer» Correct Answer - B 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.`

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