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Question Number 80739 by jagoll last updated on 05/Feb/20

$$\cos {}^3\theta +2\sin {}^2\theta =3\overline{}\theta \in (0,2\pi )$$$$whatis\theta ?$$

Commented by mr W last updated on 06/Feb/20

$$nosolution!becauseLHSmax=2<RJS!$$

Commented by hknkrc46 last updated on 06/Feb/20

$${sin}^2\theta =1-{cos}^2\theta$$$${cos}^3\theta +2(1-{cos}^2\theta )=3$$$${cos}^3\theta +2-2{cos}^2\theta =3$$$${cos}^3\theta -2{cos}^2\theta =1$$$${cos}^2\theta (cos\theta -2)=1$$$$-1⩽cos\theta ⩽1\Rightarrow -3⩽cos\theta -2⩽-1$$$$\Rightarrow {cos}^2\theta <0\Rightarrow \theta \notin (0,2\pi )$$

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