PHƢƠNG TRÌNH LƢỢNG GIÁC
Giải các phƣơng trình sau:
5x 3x
1. 4cos cos + 2(8sinx-1)cosx = 5 (D - 2010)
2 2
2. (sin2x+cos2x)cosx + 2cos2x - sinx = 0 (B - 2010)
(1 sin x cos 2 x) sin x
3. 4
1
cos x (A - 2010)
1 tan x 2
4. 3 cos5x - 2sin3xcos2x - sinx = 0 (D - 2009)
5. sinx + cosxsin2x+ 3 cos3x = 2(cos4x+ sin3x) (B - 2009)
6.
1 2 sin x cos x 3 (A - 2009)
1 2 sin x 1 sin x
7. 2sinx(1+2cos2x)+ sin2x = 1 + 2cosx (D - 2008)
8. sin3x - 3 cos3x = sinxcos2x - 3 sin2xcosx (B - 2008)
1 1 7
9. 4 sin x (A - 2008)
sin x 3 4
sin x
2
2
x x
10. sin cos 3 cos x 2 (D - 2007)
2 2
11. 2sin22x + sin7x - 1 = sinx (B - 2007)
12. (1 + sin2x)cosx + (1 + cos2x)sinx = 1 + sin2x (A - 2007)
13. cos3x + cos2x - cosx - 1 = 0 (D - 2006)
14. cot x sin x1 tan x tan 4
x
(B - 2006)
2
2 cos x sin x sin x cos x 0
6 6
15. (A - 2006)
2 2 sin x
16. cos4x + sin4x + cos x sin 3x - = 0
3
(D - 2005)
4 4 2
17. 1 + sinx + cosx + sin2x + cos2x = 0 (B - 2005)
18. cos23xcos2x - cos2x = 0 (A - 2005)
19. (2cosx - 1)(2sinx + cosx) = sin2x - sinx (D - 2004)
20. 5sinx - 2 = 3(1 - sinx)tan2x (B - 2004)
x x
sin tan x cos 0
2 2 2
21. (D - 2003)
2 4 2
2
22. cotx - tanx + 4sin2x = (B - 2003)
sin 2 x
cos 2 x 1
23. cotx - 1= sin 2 x sin 2 x (A - 2003)
1 tan x 2
24. cos3x - 4cos2x + 3cosx - 4 = 0 (D - 2002)
25. sin23x - cos24x = sin25x - cos26x (B - 2002)
cos 3 x sin 3 x
26. 5 sin x
cos 2 x 3 (A - 2002)
1 2 sin 2 x
27. 2sin2x - cos2x = 7sinx + 2cosx - 4 (ĐHQGHN - 2001)
1
28. cos3xcos3x - sin3xsin3x = cos34x + (ĐHNNHN - 2001)
4
29. sin2x + 2tanx = 3 (ĐHBKHN - 2001)
9
30. sin4x + sin4(x + ) + sin4 (x - ) = (ĐHGTVT - 2001)
4 4 8
1 2
31. 48 - 4
2
(1+cot2xcotx) = 0 (ĐHMĐC - 2001)
cos x sin x
3 x 1 3 x
32. sin
sin (ĐHThủy lợi - 2001)
10 2 2 10 2
33. sin2x - cos2x = 3sinx +cosx - 2 (ĐHNN1 - 2001)
34. 4sin3xcos3x + 4cos3xsin3x + 3 3 cos4x = 3 (HVCNBCVVT - 2001)
35. tan2xcot22xcot3x = tan2x - cot22x + cot3x (ĐH Luật - 2001)
2
36. 2
2 tan
2
x + 5tanx + 5cotx + 4 = 0 (ĐH TM - 2001)
sin x x x
4 4
37. sin 2 + cos 2 = 1 - 2sinx (ĐH Công đoàn - 2001)
38. cos 2 x + cos 2 x + 4sinx = 2 + 2 (1 - sinx) (ĐH Hàng hải - 2001)
4 4
39. sin2x + 2cos2x = 1 + sinx - 4cosx (ĐH An ninh 2001)
2 2
40. 2cos2x + sin xcosx + cos xsinx = 2(sinx + cosx) (ĐHDL PĐ - 2001)
2 2 2
41. sin x + sin 2x + sin 3x = 2 (ĐHSP TPHCM)
42. cos3x + 2 cos 3x = 2(1 + sin 2x) 2
2
(HVNH TPHCM)
1
43. sin4x + cos4x = sin2x -
2
44. 4sin3x + 4sin2x + 3sin2x + 6cosx = 0