The number of values of theta in [0, 2pi] sat | vedclass

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(A) Given equation: $2\sin^2 	heta = 4 + 3\cos 	heta$Using the identity $\sin^2 	heta = 1 - \cos^2 	heta$,we get:$2(1 - \cos^2 	heta) = 4 + 3\cos

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$0$

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(A) Given equation: $2\sin^2 	heta = 4 + 3\cos 	heta$Using the identity $\sin^2 	heta = 1 - \cos^2 	heta$,we get:$2(1 - \cos^2 	heta) = 4 + 3\cos 	heta$$2 - 2\cos^2 	heta = 4 + 3\cos 	heta$Rearranging the terms to form a quadratic equation in $\cos 	heta$:$2\cos^2 	heta + 3\cos 	heta + 2 = 0$Let $x = \cos 	heta$. The equation becomes $2x^2 + 3x + 2 = 0$.The discriminant $D$ of this quadratic equation is $b^2 - 4ac = 3^2 - 4(2)(2) = 9 - 16 = -7$.Since the discriminant is negative $(D Therefore,there are no values of $	heta$ that satisfy the given equation.Thus,the number of values is $0$.

The number of values of $\theta$ in $[0, 2\pi]$ satisfying the equation $2\sin^2 \theta = 4 + 3\cos \theta$ is

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