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Answer 1

$2 \sin 2 x - 3 \cos^{2} x + 5 \sin x . \cos x - 2 = 0 < = > 2 \sin 2 x - \frac{3}{2} - \frac{3}{2} \cos 2 x + \frac{5}{2} \sin 2 x - 2 = 0 < = > \frac{9}{2} \sin 2 x - \frac{3}{2} \cos 2 x - \frac{7}{2} = 0 < = > 9 \sin 2 x - 3 \cos 2 x = 7 < = > \frac{9}{3 \sqrt{10}} \sin 2 x - \frac{3}{3 \sqrt{10}} \cos 2 x = \frac{7}{3 \sqrt{10}} < = > \frac{3}{\sqrt{10}} \sin 2 x - \frac{1}{\sqrt{10}} \cos 2 x = \frac{7 \sqrt{10}}{30} < = > \sin 2 x . \cos a - \cos 2 x . \sin a = \frac{7 \sqrt{10}}{30} V ớ i a l à g ó c c ó \cos a = \frac{3}{\sqrt{10}}; \sin a = \frac{1}{\sqrt{10}} < = > \sin (2 x - a) = \frac{7 \sqrt{10}}{30} < = > 2 x - a = a r c \sin (\frac{7 \sqrt{10}}{30}) + k 2 π hoặc 2 x - a = π - \arcsin (\frac{7 \sqrt{10}}{30}) + k 2 π, k \in Z < = > x = \frac{1}{2} a + \frac{1}{2} \arcsin (\frac{7 \sqrt{10}}{30}) + kπ hoặc x = \frac{π}{2} + \frac{1}{2} a + \frac{1}{2} + \arcsin (\frac{7 \sqrt{10}}{30}) + kπ, k \in Z Vậy S = \{\frac{1}{2} + \arcsin (\frac{7 \sqrt{10}}{30}) + kπ; \frac{π}{2} + \frac{1}{2} a + \frac{1}{2} + \arcsin (\frac{7 \sqrt{10}}{30}) + kπ\}, k \in Z$ .

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Answer 2

$2 \sin 2 x - 3 \cos^{2} x + 5 \sin x . \cos x - 2 = 0 < = > 2 \sin 2 x - \frac{3}{2} - \frac{3}{2} \cos 2 x + \frac{5}{2} \sin 2 x - 2 = 0 < = > \frac{9}{2} \sin 2 x - \frac{3}{2} \cos 2 x - \frac{7}{2} = 0 < = > 9 \sin 2 x - 3 \cos 2 x = 7 < = > \frac{9}{3 \sqrt{10}} \sin 2 x - \frac{3}{3 \sqrt{10}} \cos 2 x = \frac{7}{3 \sqrt{10}} < = > \frac{3}{\sqrt{10}} \sin 2 x - \frac{1}{\sqrt{10}} \cos 2 x = \frac{7 \sqrt{10}}{30} < = > \sin 2 x . \cos a - \cos 2 x . \sin a = \frac{7 \sqrt{10}}{30} V ớ i a l à g ó c c ó \cos a = \frac{3}{\sqrt{10}}; \sin a = \frac{1}{\sqrt{10}} < = > \sin (2 x - a) = \frac{7 \sqrt{10}}{30} < = > 2 x - a = a r c \sin (\frac{7 \sqrt{10}}{30}) + k 2 π hoặc 2 x - a = π - \arcsin (\frac{7 \sqrt{10}}{30}) + k 2 π, k \in Z < = > x = \frac{1}{2} a + \frac{1}{2} \arcsin (\frac{7 \sqrt{10}}{30}) + kπ hoặc x = \frac{π}{2} + \frac{1}{2} a + \frac{1}{2} + \arcsin (\frac{7 \sqrt{10}}{30}) + kπ, k \in Z Vậy S = \{\frac{1}{2} + \arcsin (\frac{7 \sqrt{10}}{30}) + kπ; \frac{π}{2} + \frac{1}{2} a + \frac{1}{2} + \arcsin (\frac{7 \sqrt{10}}{30}) + kπ\}, k \in Z$ .

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