PHƯƠNG TRÌNH LƯỢNG GIÁC CỦA CÁC ĐỀ THI CÁC NĂM GẦN ĐÂY

PHƯƠNG TRÌNH LƯỢNG GIÁC
Giải các phương trình sau:
1. 4cos
2
5x
cos
2
3x
+ 2(8sinx-1)cosx = 5 (D - 2010)
2. (sin2x+cos2x)cosx + 2cos2x - sinx = 0 (B - 2010)
3.
x
x
xxx
cos
2
1
tan1
4
sin)2cossin1(
=
+






+++
π
(A - 2010)

4.
3
cos5x - 2sin3xcos2x - sinx = 0 (D - 2009)
5. sinx + cosxsin2x+
3
cos3x = 2(cos4x+ sin
3
x) (B - 2009)
6.
( )
( )( )
3
sin1sin21
cossin21
=
−+
−
xx
xx
(A - 2009)
7. 2sinx(1+2cos2x)+ sin2x = 1 + 2cosx (D - 2008)
8. sin
3
x -
3
cos
3
x = sinxcos
2
x -

3
sin
2
xcosx (B - 2008)
9.






−=






−
+ x
x
x 4
7
sin4
2
3
sin
1
sin
1

π
π
(A - 2008)
10.
2cos3
2
cos
2
sin
2
=






+
+
x
xx
(D - 2007)
11. 2sin
2
2x + sin7x - 1 = sinx (B - 2007)
12. (1 + sin
2
x)cosx + (1 + cos
2
x)sinx = 1 + sin2x (A - 2007)

13. cos3x + cos2x - cosx - 1 = 0 (D - 2006)
14.
4
2
tantan1sincot =






++
x
xxx
(B - 2006)
15.
( )
0
sin22
cossinsincos
2
66
=
−+
− x
xxxx
(A - 2006)
16. cos
4
x + sin

4
x + cos






−
4
π
x
sin






−
4
3
π
x
-
2
3
= 0 (D - 2005)
17. 1 + sinx + cosx + sin2x + cos2x = 0 (B - 2005)
18. cos

2
3xcos2x - cos
2
x = 0 (A - 2005)
19. (2cosx - 1)(2sinx + cosx) = sin2x - sinx (D - 2004)
20. 5sinx - 2 = 3(1 - sinx)tan
2
x (B - 2004)
21.
0
2
costan
42
sin
222
=






−
−
x
x
x
π
(D - 2003)
22. cotx - tanx + 4sin2x =

x2sin
2
(B - 2003)
23. cotx - 1=
xx
x
x
2sin
2
1
2sin
tan1
2cos
−+
+
(A - 2003)
24. cos3x - 4cos2x + 3cosx - 4 = 0 (D - 2002)
25. sin
2
3x - cos
2
4x = sin
2
5x - cos
2
6x (B - 2002)
26. 5
32cos
2sin21
3sin3cos

sin +=






+
+
+ x
x
xx
x
(A - 2002)
27. 2sin2x - cos2x = 7sinx + 2cosx - 4 (ĐHQGHN - 2001)
28. cos3xcos
3
x - sin3xsin
3
x = cos
3
4x +
4
1
(ĐHNNHN - 2001)
29. sin2x + 2tanx = 3 (ĐHBKHN - 2001)
30. sin
4
x + sin
4

(x +
4
π
) + sin
4
(x -
4
π
) =
8
9
(ĐHGTVT - 2001)
31. 48 -
xx sincos
24
21
−
(1+cot2xcotx) = 0 (ĐHMĐC - 2001)
32. sin






+=







−
2
3
10
sin
2
1
210
3 xx
ππ
(ĐHThủy lợi - 2001)
33. sin2x - cos2x = 3sinx +cosx - 2 (ĐHNN1 - 2001)
34. 4sin
3
xcos3x + 4cos
3
xsin3x + 3
3
cos4x = 3 (HVCNBCVVT - 2001)
35. tan
2
xcot
2
2xcot3x = tan
2
x - cot
2
2x + cot3x(ĐH Luật - 2001)

36.
x
x
tan2
sin
2
2
2
+
+ 5tanx + 5cotx + 4 = 0 (ĐH TM - 2001)
37. sin
4
2
x

+ cos
4

2
x
= 1 - 2sinx (ĐH Công đoàn - 2001)
38. cos






+
4

2
π
x
+ cos






−
4
2
π
x
+ 4sinx = 2 +
2
(1 - sinx) (ĐH Hàng hải - 2001)
39. sin2x + 2cos2x = 1 + sinx - 4cosx (ĐH An ninh 2001)
40. 2cos2x + sin
2
xcosx + cos
2
xsinx = 2(sinx + cosx) (ĐHDL PĐ - 2001)
41. sin
2
x + sin
2
2x + sin
2

3x = 2 (ĐHSP TPHCM)
42. cos3x +
x3cos
2
2
−
= 2(1 + sin
2
2x) (HVNH TPHCM)
43. sin
4
x + cos
4
x = sin2x -
2
1
44. 4sin
3
x + 4sin
2
x + 3sin2x + 6cosx = 0