If 2cos^2 x + 3sin x - 3 = 0 and 0^circ le x | vedclass

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Question

(A) Given equation: $2\cos^2 x + 3\sin x - 3 = 0$Using the identity $\cos^2 x = 1 - \sin^2 x$,we get:$2(1 - \sin^2 x) + 3\sin x - 3 = 0$$2 - 2\sin^2 x

Vedclass · Accepted Answer

$30^\circ, 90^\circ, 150^\circ$

Vedclass · Answer

(A) Given equation: $2\cos^2 x + 3\sin x - 3 = 0$Using the identity $\cos^2 x = 1 - \sin^2 x$,we get:$2(1 - \sin^2 x) + 3\sin x - 3 = 0$$2 - 2\sin^2 x + 3\sin x - 3 = 0$$-2\sin^2 x + 3\sin x - 1 = 0$$2\sin^2 x - 3\sin x + 1 = 0$Factoring the quadratic equation:$(2\sin x - 1)(\sin x - 1) = 0$This gives two cases:$1) \sin x = \frac{1}{2} \Rightarrow x = 30^\circ, 150^\circ$$2) \sin x = 1 \Rightarrow x = 90^\circ$Thus,the values of $x$ are $30^\circ, 90^\circ, 150^\circ$.

If $2\cos^2 x + 3\sin x - 3 = 0$ and $0^\circ \le x \le 180^\circ$,then $x =$

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