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Answer 1 · 2016-12-12T13:58:14

$2 {sin}^{2} θ + 3 {cos}^{2} θ$ $2sin^2theta+3cos^2theta$

$= 2 {sin}^{2} θ + 2 {cos}^{2} θ + {cos}^{2} θ$ $=2sin^2theta+2cos^2theta+cos^2theta$

$= 2 ({sin}^{2} θ + {cos}^{2} θ) + {cos}^{2} θ$ $=2(sin^2theta+cos^2theta)+cos^2theta$

$= 2 \cdot 1 + {cos}^{2} θ$ $=2*1+cos^2theta$

The value of given expression will be minimum when ${cos}^{2} θ$ $cos^2theta$ minimum which is $= 0$ $=0$ . So the minimum value is $= 2$ $=2$