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
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