PT Luong Giac

PTLG_Quach duy tuan

Chuyên Đề 1:
PT bậc 2 với một HSLG


1) 2sin
2
x - cos
2
x - 4sinx + 2 = 0
2) 9cos
2
x - 5sin
2
x - 5cosx + 4 = 0
3) 5sinx(sinx - 1) - cos
2
x = 3
4) cos
2
(3x +
2

) cos
2
3x 3cos(
2

- 3x) + 2 = 0
5)[cđsphn_97] cos2x + sin

2
x + 2cosx + 1 = 0
6) 3cos2x + 2(1 +
2
+ sinx)sinx (3 +
2
) = 0
7) tg
2
x + (
3
- 1)tgx
3
= 0
8)
3cot3
sin
3
2
+=
gx
x
9)[ĐHKT TPHCM_90]
2
2cos2cot
4sin2cot32cos
=

++
xxg

xxgx
10)[ĐHBKHN_94]
0
cos
2cos39sin62sin4
22
=
+
x
xxx
11)[ĐH Thuỷ Sản Nha Trang_01]
1
12sin
)2(sinsin3)sin2(coscos
=

+++
x
xxxxx
Chuyên Đề 2:
PT bậc 3 với một HSLG
1) 4sin
3
x 8sin
2
x + sinx + 3 = 0
2)[ĐH Luật HN_00] 4(sin3x cos2x) = 5(sinx 1)
3)
032cos)334(cos)326(cos4
23

=+++
xxx
4) cos3x + 3cos2x = 2(1 + cosx)
5) 2tg
3
x + 5tg
2
x 23tgx + 10 = 0
6)
03)33()323(6
23
=+++
tgxxtgxtg
7) tg3x tgx = 2
8) cotg
3
x + 2cotg
2
x 3cotgx - 6 = 0
9) 2cotg
3
x cotg
2
x 13cotgx 6 = 0
10)[ĐHNN HN_00] 2cos2x 8cosx + 7 = 1/cosx

Chuyên Đề 3:
PT bậc nhất đối với Sin và cos
1)
23sin3cos3

=+
xx

2)[ĐH Mỏ_95]
xxx 3sin419cos33sin3
3
+=

3)[ĐH Mỹ Thuật Công Nghiệp HN_96]
xxxxx 5sin7sin12sin35cos7cos
=

4)[ĐHKT_97] Tìm các nghiệm x
)
7
6
;
5
2
(


của PT

27sin37cos
=
xx

5)[ĐHGT_00]
xxxx 2cos3cos)cos(sin22

+=+
6)
0)
6
5sin(5)
6
sin(4)
3
sin(3
=++++

xxx
7)[HVCNBCVT_01]
34cos333sincos43cossin4
33
=++
xxxxx
8) 2sin4x + 3cos2x + 16sin
3
xcosx 5 = 0
9)[CĐHQ TPHCM_98] 4sin
3
x 1= 3sinx -
3
cos3x
10)[ĐH Kỹ Thuật Công Nghệ TPHCM_00]
cos
2
x -
3

sin2x = 1 + sin
2
x
11)[ĐH Văn Lang TPHCM_98]
4(sin
4
x + cos
4
x) +
3
sin4x = 2
12)[ĐHNN I_95]
xxxx cos3sin2sin32cos2
+=++
13)[ĐHTM_00]
xxx 2cos222cos22sin3
2
+=
14)[ĐHSP Quy Nhơn_98]
2cos3sincos3sin
=+++
xxxx
Chuyên Đề 4:
PT đcấp bậc 2 đối với sin và cos
1) sin
2
x + 2sinxcosx + 3cos
2
x - 3 = 0
2) sin

2
x 3sinxcosx + 1 = 0
3) 4
3
sinxcosx + 4cos
2
x = 2sin
2
x + 5/2
4)
)
2
cos()
2
5
sin(2)3(sin3
2
xxx
+++



0)
2
3
(sin5
2
=+
x

5)[ĐHAN_98]
a.
x
xx
cos
1
cossin3
=+
b.
x
xx
cos
1
cos6sin4
=+
6) cos
2
x 3sinxcosx 2sin
2
x 1 = 0
7) 6sin
2
x + sinxcosx cos
2
x = 2
Chuyên Đề 5:
PT đcấp bậc 3 đối với sin và cos
1)[ĐHL_96] 4sin
3
x + 3cos

3
x 3sinx sin
2
xcosx =
0
2)[ĐHNT_96] cos
3
x 4sin
3
x 3cosxsin
2
x + sinx = 0
3)[ĐH Huế_98] cos
3
x + sinx 3sin
2
xcosx = 0
4)[ĐH Đà Nẵng_99] cos
3
x sin
3
x = sinx cosx
5)[CĐSPTW1_01] 4cos
3
x + 2sin
3
x 3sinx = 0
6)[HVKTQS_96] 2cos
3
x = sin3x

7)[ĐHD TPHCM_97] sinxsin2x + sin3x = 6cos
3
x
8)[ĐHY HN_99] sinx + cosx - 4sin
3
x = 0
9)[ĐHQGHN_96] 1 + 3sin2x = 2tgx
10)[ĐHNN B_99] sin
2
x(tgx + 1) = 3sinx(cosx sinx)
+3
11)[PVBCTT_98]
xx sin2)
4
(sin2
3
=+

12)[ĐHQGHN_98]
xx 3cos)
3
(cos8
3
=+


13)[ĐHQG TPHCM_98]
xx sin2)
4
(sin

3
=

14)[ĐHYHN_95]
x
xx
xx
2cos2
cos4sin5
cos2sin6
3
=
Chuyên Đề 6:
PT đối xứng và nửa đối xứng
Với sin và cos
1)
2
(sinx + cosx) - sinxcosx = 1
2) (1 sinxcosx)(sinx + cosx) =
2
2
3)
3
10
sin
1
sin
cos
1
cos

=+++
x
x
x
x
4) sin
3
x + cos
3
x =
2
2
5) 1 + sin
3
x + cos
3
x =
2
3
sin2x
6)[HVCTQG TPHCM] 2sin2x 2(sinx + cosx) +1 = 0
7)[ĐH Huế D_00] sinxcosx + 2sinx + 2cosx = 2
8)[ĐHM_99] 1 + tgx = 2
2
sinx
1
PTLG_Quach duy tuan

9) sinx + cosx =
xx cossin1

3
32
+
10) sinx cosx + 7sin2x = 1
11)
21cossin2)cos)(sin21(
+=++
xxxx
12)[ĐHNN_00]
1)
4
sin(22sin
=+

xx
13)
12sin4cossin
=+
xxx
Chuyên Đề 7:
PTLG đối xứng với tg và cotg
1)
3
(tgx + cotgx) = 4
2)[ĐHCĐ_97]
2
(sinx + cosx) = tgx + cotgx
3)[ĐHNN_97] cotgx tgx = sinx + cosx
4)[ĐH Cần Thơ_D99] 3(tgx + cotgx) = 2(2 + sin2x)
5)[ĐHGT_95] tg2x + cotgx = 8cos

2
x
6)[ĐHQG_B96] tgx = cotgx + 2cotg
3
2x
7)[ĐH Đông Đô_97] tgx + cotgx = 2(sin2x + cos2x)
8)[ĐH Đông Đô_99] cotgx = tgx + 2tg2x
9)[97II] 6tgx + 5cotg3x tg2x
10)[ĐHYHN_98] 2(cotg2x cotg3x) = tg2x + cotg3x
11)[ĐHQG TPHCM_A96] tg
2
x tgxtg3x = 2
12)[ĐHTH_A93] 3tg2x 4tg3x = tg
2
3xtg2x
13)[CĐ Hải Quan_00]
3tg
2
x + 4tgx + 4cotgx + 3cotg
2
x +2 = 0
14) tgx + tg
2
x + tg
3
x + cotgx + cotg
2
x + cotg
3
x = 6

15) tg2x tg3x tg5x = tg2xtg3xtg5x
16) tg
2
2xtg
2
3xtg5x = tg
2
2x tg
2
3x + tg5x
17)[ĐHDHN_01]
tg
2
x.cotg
2
2x.cotg3x = tg
2
x cotg
2
2x + cotg3x
18)[CĐGT_01]
tg
2
x.tg
2
3x.tg4x = tg
2
tg
2
3x + tg4x

19)[ĐHNT TPHCM_97] 2tgx + cotgx =
xsin
2
3
+
20)[71 III] 3tg3x + cotg2x = 2tgx +
x4sin
2

21)[ĐHQG_A98] 2tgx +cotg2x = 2sin2x +
x2sin
1

22) 3tg6x -
x8sin
2
= 2tg2x cotg4x
23)[130 III] cotg2x + cotg3x +
xxx 3sin2sinsin
1
= 0
24)[ĐHBK_98]
1cot
)sin(cos2
2cot
1


=
+

gx
xx
xgtgx
25)
)cot(3212)
cos
1
sin
1
(3
22
gxtgx
xx
=+

26)[ĐHBKHN_00]
)cot(
2
1
2sin
cossin
44
gxtgx
x
xx
+=
+
Chuyên Đề 8:
PTLG Đxứng đối với sin
2n

và
cos
2n

1)[ĐHBKHN_96] sin
4
x + cos
4
x = cos2x
2)[ĐH Huế_99] sin
6
x + cos
6
x = 7/16
3) sin
6
x + cos
6
x =
x2sin
4
1
2
4) sin
6
x + cos
6
x = cos4x
5)[HVCTQG TPHCM_00]
16(sin

6
x + cos
6
x 1) + 3sin6x = 0
6)[ĐHQG_98] cos
6
x sin
6
x =
8
13
cos
2
2x
7)[ĐHKT_95]
8
5
)
3
(cos)
3
(sin
44
=+
xx
8)[ĐHCĐ_01]
x
xx
sin21)
2

(cos)
2
(sin
44
=+
9)
8
3
3sin
1
3cos
1
22
=
xx
Chuyên Đề 9:
sử dụng ct hạ bậc

1) cos
2
x + cos
2
2x + cos
2
3x = 3/2
2) cos
2
x + cos
2
2x + cos

2
3x = 1
3)[ĐH Huế] sin
2
x + sin
2
2x + sin
2
3x = 3/2
4)[ĐHY_98] sin
2
3x sin
2
2x sin
2
x = 0
5)[ĐHQG_98] sin
2
x = cos
2
2x + cos
2
3x
6)[ĐH_B02] sin
2
3x cos
2
4x = sin
2
5x cos

2
6x
7) cos
2
x + cos
2
2x + cos
2
3x + cos
2
4x = 2
8) cos
2
x + cos
2
2x + cos
2
3x + cos
2
4x = 3/2
9)[Đ52II] cos
2
x = cos
3
4x
10)[Đ15III]
5
4
cos3
5

3
cos21
2
xx
=+
11)[Đ48II] sin
2
2x cos
2
8x =
)10
2
17
sin( x
+

12)[ĐHD_99] sin
2
4x cos
2
6x =
)105,10sin( x
+

13)[ĐHTDTT_01]
cos3x+sin7x=
2
9
cos2)
2

5
4
(sin2
22
xx
+

14)[ĐHHH_95] sin
4
x +
4
1
)
4
(cos
4
=+

x
15)[ĐHBKHN_95]
2sin
2
x(4sin
4
x 1) = cos2x(7cos
2
2x + 3cos2x 4)
16)[ĐHXD_97]
x
xtgxtg

xx
4cos
)
4
()
4
(
2cos2sin
4
44
=
+
+


11)[ĐHGT_99]
sin
4
x + cos
4
x =
)
6
(cot)
3
(cot
8
7
xgxg
+

12)[ĐHGT_01]
Sin
4
x +
8
9
)
4
(sin)
4
(sin
44
=++

xx
13)[ĐHNT TPHCM_95] sin
8
x + cos
8
x=
16
17
cos
2
2x
14)[HVKTMM_99] sin
8
x + cos

8
x =
32
17
15)[Vô Địch New York_73]
sin
8
x + cos
8
x =
128
97

16)[HVQY_97] sin
8
2x + cos
8
2x = 1/8
17)[ĐHKT_99] sin
2
x + sin
2
3x = cos
2
2x + cos
2
4x
18)[Đ135II] cos
3
xcos3x + sin

3
xsin3x =
4
2
2
PTLG_Quach duy tuan

19)[Đ142III] cos
3
xcos3x + sin
3
xsin3x = cos
3
4x
20)[ĐHNT_99] cos
3
xsin3x + sin
3
xcos3x = sin
3
4x
21)[HVBCVT_01]
4sin
3
xsin3x + 4sin
3
xcos3x + 3
3
cos4x = 3
22)[ĐHSP TPHCM_00]

2cos
2
x + 2cos
2
2x + 2cos
2
3x 3 = cos4x(2sin2x +
1)
23)[ĐHN_01]
cos
3
xcos3x sin
3
xsin3x = cos
3
4x + 1/2
Chuyên Đề 10:
sử dụng CT góc nhân đôi
1)[ĐHY_97] cos
4
x + sin
6
x = cos2x
2)[ĐHNN_97] cos2x + 5sinx + 2 = 0
3)[ĐHNN_99] 2sin
3
x cos2x + cosx = 0
4)[Đ68II] 2cos
3
x + cos2x + sinx = 0

5)[Đ72II] cos
4
x cos2x + 2sin
6
x = 0
6)[ĐHNT_95] 4cosx 2cos2x cos4x = 1
7)[ĐHHH_99] cos2x + 5 = 2(2 cosx)(sinx- cosx)
8)[ĐHYHN_00] sin
3
x + cos
3
x = cos2x
9)[ĐH Huế_98] 2sin
3
x + cos2x = sinx
10)[ĐHQGHN_95] 4sin2x 3cos2x = 3(4sinx 1)
11)[Đ16III] Tìm nghiệm
)3;
2
(



x
của PT sau
xxx sin21)
2
7
cos(3)
2

5
2sin(
+=+


12)[Đ81III]
)
24
(cos2sin
2
cossin
2
sin1
22
x
x
x
x
x
=+

13)[ĐHQGHN _98] sin
3
x + cos
3
x = 2(sin
5
x + cos
5
x)

14)[ĐHNT_00]
sin
8
x + cos
8
x = 2(sin
10
x + cos
10
x) +
4
5
cos2x
15)[HVCNBCVT_98] sin4x cos4x = 1 + 4(sinx
cosx)
16)[Đ97II] 6tgx = tg2x
17)[HVNH TPHCM_98] 2 + cosx =
2
2
x
tg
18)[ĐHTC_97] (1 tgx)(1 + sin2x) = 1 + tgx
19)[ĐHM_99] tgxsin
2
x 2sin
2
x = 3(cos2x +
sinxcosx)
20)[ĐHQGHN_D00] 1 + 3tgx = 2sin2x
21)[viện ĐH Mở HN_98] cosx +

2
x
tg
= 1
22)[ĐH Dân Lập Đông Đô_99] cotgx = tgx + 2tg2x
Chuyên Đề 11:
sử dụng CT góc nhân ba
1)[ĐHY Hải Phòng_00] sin3x + sin2x = 5sinx
2) sin3x + sinx 2cos
2
x = 0
3)[ĐHY Thái Nguyên] 4cos
2
x
cos3x=6cosx+2(1+cos2x)
4)[Đ76II]
cos10x+2cos
2
4x+6cos3xcosx = cosx +8cosxcos
3
3x
5) 32cos
6
x cos6x = 1
6)[ĐHTH_B92] 2sin3x(1 4sin
2
x) = 1
7)[ĐHQGHN_01]
sin3x = cosxcos2x(tg
2

x + tg2x)
8)[ĐHTM_99]
x
x
x
x
cos
1
3cos2
sin
1
3sin2
+=
9)[ĐHTL_01]
)
2
3
10
sin(
2
1
)
210
3
sin(
xx
+=

10)[HVCNBCVT_99]
)

4
sin(2sin)
4
3sin(

+=
xxx
11)[ĐHQG_99]
xx 3cos)
3
(cos8
3
=+

12)[HVNH TPHCM_00]
sin3x + cos3x + 2cosx = 0
Chuyên Đề 12:
biến đổi tổng, hiệu

thành
tích và phân tích ra thừa số
1) sinx + sin2x + sin3x = 1 + cosx + cos2x
2) sinx + sin2x + sin3x = cosx + cos2x + cos3x
3)[ĐH Nông Lâm TPHCM_01]
1 + cosx + cos2x + cos3x = 0
4)[HVQHQT_99] cosx + cos2x + cos3x + cos4x = 0
5)[ĐHSP Vinh_97]
sinx + sin2x + sin3x + sin4x + sin5x + sin6x = 0
6)[ĐH Đà Nẵng_B97] sin3x sinx + sin2x = 0
7) cos10x cos8x cos6x + 1 = 0

8)[HVQHQT_00] cosx + cos3x + 2cos5x = 0
9)[ĐHNTHN_97] 9sinx + 6cosx 3sin2x + cos2x = 8
10)[ĐHNT TPHCM_00]
1 + sinx + cos3x = cosx + sin2x + cos2x
11)[ĐHYHN_00] sin4x = tgx
12) (2sinx 1)(2sin2x + 1) = 3 4cos
2
x
13)[ĐHYHN_96] (cosx sinx)cosxsinx = cosxcos2x
14)[ĐHHH_00]
(2sinx + 1)(3cos4x + 2sinx 4) + 4cos
2-
x = 3
15)[ĐH Đà Nẵng_99] cos
3
x sin
3
x = sinx cosx
16)[ĐH Thuỷ Sản Nha Trang_96]
cos
3
x + sin
3
x = sinx cosx
17)[ĐHCSND_00] cos
3
x + sin
3
x = sin2x + sinx +cosx
18)[HVQY_00] cos

2
x + sin
3
x + cosx = 0
19)[HVNH_99] cos
3
x + cos
2
x + 2sinx 2 = 0
20)[HVNH TPHCM_00] sinx + sin
2
x + cos
3
x = 0
21)[HVBCVT TPHCM_97] cos
2
x 4sinxcosx = 0
22)[HVKTQS_99] 2sin
3
x sinx =2cos
3
x cosx +
cos2x
23)[ĐHSPI_00] 4cos
3
x +3
2
sin2x = 8cosx
24)[ĐHNTHN_98]
sinx +sin

2
x +sin
3
x +sin
4
x =cosx+cos
2
x+cos
3
x+cos
4
x
25)[ĐH Thuỷ Sản Nha Trang_97]
x
xx
2sin
2
sin
2
cos
44
=
26)[HVQY_97]
01
2
sin)3(sin
2
sin)3(sin
24
=+++

x
x
x
x
27)[ĐHQGHN_B97]
xx
x
cos
1
sin
1
)
4
sin(22
+=+

28)[ĐHKTHN_98]
xxx 4sin
2
2sin
1
cos
1
=+
29)[ĐHTL_00] 5sin3x = 3sin5x
3
PTLG_Quach duy tuan

30)[ĐHM_97]
1

sin5
5sin
=
x
x
31)[ĐHNNHN_00] 2cos2x 8cosx + 7 = 1/cosx


Chuyên Đề 13:
sd CT biến đổi tích thành
tổng
1) cos11x.cos3x = cos17x.cos9x
2) sin18x.cos13x = sin9x.cos4x
3) sin
2
x + sin2xsin4x + sin3xsin9x + sin4xsin16x = 1
4) (sinx +
3
cosx)sin3x = 2
5)
xxxx 2cos)
6
sin()
6
sin(cos4
=+

6)[ĐHBK TPHCM_91]
sin3x -
3

2
sin
2
x = 2sinxcos2x
7) 8sinx =
xx sin
1
cos
3
+
8)[ĐHGT_96] cos3xtg5x = sin7x
9)
)
3
2
cos(.cos34)
3
sin().
3
sin(.sin4

+++
xxxxx
.

2)
3
4
cos(
=+

x
10)[ĐHTHHN_92] 2sin3x(1 4sin
2
x) = 1
11)[ĐHDHN_00]
cos2x + cos4x + cos6x = cosxcos2xcos3x + 2
12)[ĐHYHN_97]
2
1
2
3
sin
2
sinsin
2
3
cos
2
coscos
=
xx
x
xx
x
13)[HVQHQT_96]
2
sincos5
2
5

sin
3
x
x
x
=
14)[ĐHTL TPHCM_00]
tgx 3cotgx = 4(sinx +
)cos3 x

15)[ĐHKT_00]
xxx 2cos2sin81)
4
3sin(2
2
+=+

Chuyên Đề 14:
PTLG phối hợp(tg,sin),
(cotg,cos)
1) 2(tgx sinx) + 3(cotgx cosx) + 5 = 0
2)[ĐHGT_97] 3(cotgx cosx) 5(tgx sinx) = 2
3)[ĐHDL Hồng Đức Thanh Hoá_99]
4sin
2
x + 3tg
2
x = 1
4)[ĐHM_99] 1 + tgx =
xsin22

5)[ĐHQG_96] 1 + 3sin2x = 2tgx
6)[ĐHQGHN_95] tg
2
x(1 sin
3
x) + cos
3
x 1 = 0
7)[ĐHQG_A00] 2sinx + cotgx = 2sin2x + 1
8)ĐH Nông Lâm TPHCM_97]
x
x
xtg
sin1
cos1
2

+
=
9)[ĐH Thuỷ Sản Nha Trang_97]
x
x
xg
cos1
sin1
cot
2
+
+
=

10) tg
2
x =
x
x
sin1
cos1


11)[CĐHQ_96] tg
2
x =
x
x
3
3
sin1
cos1


12) tg
2
x =
x
x
3
3
sin1
cos1
+

+
13)[Viện ĐH Mở_96]
x
tgx
tgx
2sin1
1
1
+=
+

14)[ĐHSP Vinh_98] 1 + cotg2x =
x
x
2sin
2cos1
2

15)[Đ56II] Tìm tổng các nghiệm x
]70;1[

của PT
cos2x tg
2
x =
x
xx
2
32
cos

1coscos


16)[Đ140II] Tìm tổng các nghiệm x
]40;2[

của PT
2cos
2
x + cotg
2
x =
x
x
2
3
sin
1sin
+
Chuyên Đề 15:
PTLG dạng phân thức
1)[Đ30II]
xxx 4sin
2
2sin
1
cos
1
=+
2)[ĐHNN_B98]

3
1sincos2
cossin2cos
2
=
++

xx
xxx
3)[ĐH Huế_A99]
1
9cos
5cot.sin
=
x
xgx
4)[Đ119II]
x
x
x
x
4cos1
4sin
2sin2
4cos1
+
=

5)[Đ90III]
3

3cos2coscos
3sin2sinsin
=
++
++
xxx
xxx
6)
0
2sin)cos(sin
2cos4cossin2
2
=

+
xxx
xxx
7)[Đ99II]
1
1cossin2
2sinsin23sin21
2
=

++
xx
xxx
8)[Đ2II]
3
10

sin
1
sin
cos
1
cos
=+++
x
x
x
x
9)[Đ18III]
6
1sin4cos3
6
sin4cos3
=
++
++
xx
xx
10)[ĐHSP Vinh_98] 1 + cotg2x =
x
x
2sin
2cos1
2

11) tg3x.cotgx = -1
4