The maximum value of the expression `1/(sin^2 theta + 3 sin theta cos – InterviewSolution

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1.	The maximum value of the expression `1/(sin^2 theta + 3 sin theta cos theta + 5cos^2 theta)` isA. 2B. 3C. 4D. 6
Answer» Correct Answer - A `sin^(2)theta+3sintheta costheta+5cos^(2)theta` `=1/2{1-cos2theta+3sin2theta+5(1+cos2theta}` `=3+2cos2theta+3/2sin2theta` Clearly, `-sqrt(4+(9)/(4))le2cos2theta+3/2sin2thetalesqrt(4+(9)/(4))` `implies-5/2le2cos2theta+3/2sin2thetale5/2` `implies2/11le(1)/(sin^(2)theta+3sinthetacostheta+5cos^(2)theta)le2` Hence, the maximum value of the given expression is 2.

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