Question

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Answer 1

$6 \sin^{2} x + 7 \sqrt{3} \sin 2 x - 8 \cos 2 x = 6 < = > 3 - 3 \cos 2 x - 8 \cos 2 x + 7 \sqrt{3} \sin 2 x - 6 = 0 < = > 7 \sqrt{3} \sin 2 x - 11 \cos 2 x - 3 = 0 < = > \frac{7 \sqrt{3}}{\sqrt{268}} \sin 2 x - \frac{11}{\sqrt{268}} \cos 2 x = \frac{3}{\sqrt{268}} < = > \sin 2 x . \cos a - \cos 2 x . \sin a = \frac{3 \sqrt{268}}{268} V ớ i a l à g ó c c ó \cos a = \frac{7 \sqrt{3}}{\sqrt{268}}; \sin a = \frac{11}{\sqrt{268}} < = > \sin (2 x - a) = \frac{3 \sqrt{268}}{268} < = > 2 x - a = a r c \sin (\frac{3 \sqrt{268}}{268}) + k 2 π hoặc 2 x - a = π - \arcsin (\frac{3 \sqrt{268}}{268}) + k 2 π, k \in Z < = > 2 x = a + \arcsin (\frac{3 \sqrt{268}}{268}) + k 2 π hoặc 2 x = π + a - \arcsin (\frac{3 \sqrt{268}}{268}) + k 2 π, k \in Z < = > x = \frac{1}{2} a + \frac{1}{2} \arcsin (\frac{3 \sqrt{268}}{268}) + kπ hoặc x = \frac{π}{2} + \frac{1}{2} a - \frac{1}{2} \arcsin (\frac{3 \sqrt{268}}{268}) + kπ, k \in Z Vậy S = \{\frac{1}{2} a + \frac{1}{2} \arcsin (\frac{3 \sqrt{268}}{268}) + kπ; \frac{π}{2} + \frac{1}{2} a - \frac{1}{2} \arcsin (\frac{3 \sqrt{268}}{268}) + kπ\}, k \in Z$ .

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Answer 2

$6 \sin^{2} x + 7 \sqrt{3} \sin 2 x - 8 \cos 2 x = 6 < = > 3 - 3 \cos 2 x - 8 \cos 2 x + 7 \sqrt{3} \sin 2 x - 6 = 0 < = > 7 \sqrt{3} \sin 2 x - 11 \cos 2 x - 3 = 0 < = > \frac{7 \sqrt{3}}{\sqrt{268}} \sin 2 x - \frac{11}{\sqrt{268}} \cos 2 x = \frac{3}{\sqrt{268}} < = > \sin 2 x . \cos a - \cos 2 x . \sin a = \frac{3 \sqrt{268}}{268} V ớ i a l à g ó c c ó \cos a = \frac{7 \sqrt{3}}{\sqrt{268}}; \sin a = \frac{11}{\sqrt{268}} < = > \sin (2 x - a) = \frac{3 \sqrt{268}}{268} < = > 2 x - a = a r c \sin (\frac{3 \sqrt{268}}{268}) + k 2 π hoặc 2 x - a = π - \arcsin (\frac{3 \sqrt{268}}{268}) + k 2 π, k \in Z < = > 2 x = a + \arcsin (\frac{3 \sqrt{268}}{268}) + k 2 π hoặc 2 x = π + a - \arcsin (\frac{3 \sqrt{268}}{268}) + k 2 π, k \in Z < = > x = \frac{1}{2} a + \frac{1}{2} \arcsin (\frac{3 \sqrt{268}}{268}) + kπ hoặc x = \frac{π}{2} + \frac{1}{2} a - \frac{1}{2} \arcsin (\frac{3 \sqrt{268}}{268}) + kπ, k \in Z Vậy S = \{\frac{1}{2} a + \frac{1}{2} \arcsin (\frac{3 \sqrt{268}}{268}) + kπ; \frac{π}{2} + \frac{1}{2} a - \frac{1}{2} \arcsin (\frac{3 \sqrt{268}}{268}) + kπ\}, k \in Z$ .

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