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Tìm nghiệm dương nhỏ nhất của phương trình: sin2x + cos2x + 3sinx – cosx – 2 = 0

Các nghiệm của phương trình $2(1+\mathrm{cosx})(1+{\cot }^2\mathrm{x})=\frac{\mathrm{sinx}-1}{\mathrm{sinx}+\mathrm{cosx}}$ được biểu diễn bởi bao nhiêu điểm trên đường tròn lượng giác?

Phương trình $\frac{\left(1-2\mathrm{cosx}\right)\left(1+\mathrm{cosx}\right)}{\left(1+2\mathrm{cosx}\right).\mathrm{sinx}}=1$ có bao nhiêu nghiệm thuộc khoảng (0; 2018π)

Tìm số nghiệm thuộc khoảng ($\frac{\mathrm{\pi }}{2}$; 3π) của phương trình: 

sin(2x + $\frac{5\mathrm{\pi }}{2}$) - 3cos(x - $\frac{7\mathrm{\pi }}{2}$) = 1 + 2sinx (*)

Phương trình tanx + tan(x + $\frac{\mathrm{\pi }}{3}$) + tan(x + $\frac{2\mathrm{\pi }}{3}$) = 3$\sqrt{3}$ tương đương với phương trình.