If 2 cos^{2} theta + 3 cos theta = 2,then the | vedclass

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(C) Given the equation: $2 \cos^{2} 	heta + 3 \cos 	heta = 2$ Rearranging the terms: $2 \cos^{2} 	heta + 3 \cos 	heta - 2 = 0$ Factoring the quadr

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$\frac{1}{2}$

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(C) Given the equation: $2 \cos^{2} 	heta + 3 \cos 	heta = 2$ Rearranging the terms: $2 \cos^{2} 	heta + 3 \cos 	heta - 2 = 0$ Factoring the quadratic equation: $2 \cos^{2} 	heta + 4 \cos 	heta - \cos 	heta - 2 = 0$ $2 \cos 	heta(\cos 	heta + 2) - 1(\cos 	heta + 2) = 0$ $(2 \cos 	heta - 1)(\cos 	heta + 2) = 0$ This gives two possible values: $\cos 	heta = \frac{1}{2}$ or $\cos 	heta = -2$ Since the range of the cosine function is $[-1, 1]$,the value $\cos 	heta = -2$ is not possible. Therefore,the permissible value is $\cos 	heta = \frac{1}{2}$.

If $2 \cos^{2} \theta + 3 \cos \theta = 2$,then the permissible value of $\cos \theta$ is

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