Giải các phương trình lượng giác sau:

1. $\sin 2x-\cos 2x+3\sin x-\cos x-1=0$
2. $\sin^{2}\left (\dfrac{x}{2} -\dfrac{\pi}{4} \right ) \tan^{2}x-\cos^{2}\dfrac{x}{2}=0$
3. $(2\cos x-1)(2\sin x+\cos x)=\sin2x-\sin x$
4. $\cos^{4} x+\sin^{4}x+\cos\left ( x-\dfrac{\pi}{4} \right )\sin \left ( 3x-\dfrac{\pi}{4} \right )-\dfrac{3}{2}=0$
5. $\cos3x+\cos2x-\cos x-1=0$
6. $\left (\sin\dfrac{x}{2}+\cos\dfrac{x}{2}\right )^{2}+\sqrt{3}\cos x=2$
7. $\sin^23x-\cos^24x=\sin^25x-\cos^26x$
8. $\cot x-\tan x+4\sin2x=\dfrac{2}{\sin 2x}$
9. $5\sin x-2=3(1-\sin x)\tan^2x$
10. $1+\sin x+\cos x+\sin2x+\cos2x=0.$
11. $\cot x+\sin x (1+\tan x \tan\dfrac{x}{2})=4$
12. $2\sin^22x+\sin7x-1=\sin x$
13. $\sin^3x-\sqrt3 \cos^3x=\sin x\cos^2x-\sqrt{3}\sin^2x\cos x$
14. $\sin x+\cos x\sin2x+\sqrt3\cos3x=2(\cos4x+\sin^3x)$
15. $(\sin2x+\cos2x)\cos x+2\cos2x-\sin x=0$
16. $\cot x -1=\dfrac{\cos 2x}{1+\tan x}+\sin^2x-\dfrac{1}{2}\sin2x$
17. $\dfrac{2 (\cos^6x+\sin^6x)-\sin x \cos x}{\sqrt{2} -2\sin x}=0$
18. $(1+\sin^2x)\cos x+(1+\cos^2x)\sin x=1+\sin2x$