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(1)11a1 thpt tien lu PHƯƠNG TRÌNH LƯỢNG GIÁC
TRONG CÁC ĐỀ THI ĐẠI HỌC TỪ 2002 ĐẾN 2009
[ĐH A02] Tìm x0;2:5 sin x cos 3x sin 3x cos 2x 2sin 2x
[ĐH B02] sin 3x cos 4x sin 5x cos 6x2 2
[ĐH D02] Tìm x0;14 cos 3x cos 2x 3cos x 0
[ĐH A03] cot x 1 cos 2x sin x2 1sin 2x
1 tan x
[ĐH B03] cot x tan x 4sin 2x sin 2x
[ĐH D03] sin2 x tna2x cos2 x
2
[ĐH B04] 5sin x 3(1 sin x) tan x2
[ĐH D04] 2 cos x 2sin x cos x sin 2x sin x
[ĐH A05] cos 3x cos 2x cos x2 0
[ĐH B05] sin cos x sin 2x cos 2x 0
[ĐH D05] cos x sin x cos x4 sin 3x
4
[ĐH A06]
6
2 cos x sin x sin x cos x 2sin x
[ĐH D06] cos3x cos 2x cos x 0
[ĐH B06] cot x sin x tan x tanx
[ĐH A07] 1 sin x cos x 1 cos x sin x sin 2x
[ĐH B07]
2sin 2x sin 7x sin x
[ĐH D07]
2
x x
sin cos cos x
2
[ĐH A08]
1
4sin x
3
sin x
sin x
[ĐH B08] sin x3 3 cos x sin x cos x3 3 sin x cos x2
[ĐH D08] 2sin x cos 2x sin 2x cos x
[CĐ 08] sin 3x cos 3x2sin 2x
[ĐH A09] (1 2sin x)cos x
(1 2sin x)(1 sin x)
[ĐH B09] sin x cos x sin 2x cos 3x2 cos 4x sin x
[ĐH D09] cos 5x 2sin 3x cos 2x sin x 0
[CĐ 09] (1 2sin x) cos x sin x cos x2
(2)Bai tap
Ví dụ : Giải phương trình :
a cos3xcos2x cosx10
b 4cos3 cos2 4cos
x x
x
c 2cos2 8cos cos
x x
x
d sin4 cos22
x
x
Ví dụ : Giải phương trình : a sin cos3 3sin 2x
2
x x b sin3 cos3 2(sin cos )
x x x
x
Ví dụ : Giải phương trình :
a cos3xcos2x cosx10
b 4cos3 x cos2x 4cosx10
c 2cos2x 8cosx 7 cos1x
d sin4xcos22x2
Ví dụ : Giải phương trình :
a) cosx sinx1 b) cosx 3sinx
c) 4(sin4 xcos )4x sin 4x2 d)
x tgx
cos
e) sin cos
2
2 sin cos
2
x x
x x
Ví duï :
a) 2 cos2 x 5sinx 4 0
b) cos2x cosx250
c) 2sin2 x 4 5cosx
d) cos cos2x x 1 cos2xcos3x
e) sin4 cos4 sin 2
x x x f) )
cos( ) cos (sin
2 4
x x
x
g) sin4 2xcos4 2x 1 2sinx h) sin4xcos4 xsinx.cosx0
k) Giải phương trình:
a) 1 cos4x sin4x 2 cos2x
c) 4(sin4xcos4x)sin4x 20
b) sin6 x cos6 x cos4x
d) sin cos3x x cos sin3x x14
e) ) ( sin
cotgx x tgxtg x
l) ) cos2
sin
3 sin cos (sin
5
x
x x x
x
GIẢI PHƯƠNG TRÌNH
1/ sin2 x+sin23x=cos22x+cos24x ; ; 10 2
k k
x k
2/ cos
2x+cos22x+cos23x+cos24x=3/2 ;
8
k
x k
3/sin2x+ sin23x-3 cos22x=0 ;
3
x kk
4/ cos3x+ sin7x=2sin2(
4
x
)-2cos29
2
x
; ;
12
k k
x k
5/ sin24x+ sin23x= cos22x+ cos2x vớix(0; ) ;
4 10 k l x
(3)6/sin24x-cos26x=sin(10,510x) với (0; )
2
x ;3 ; ;9 20 20 20 x
7/ cos
4x-5sin4x=1 x k
8/4sin3x-1=3- 3cos3x ;
6 18
k k
x
9/ sin
22x+ sin24x= sin26x ;
4 12
k k
x
10/ sin2x= cos22x+ cos23x ; ;
4 2
k
x k k
11/ (sin
22x+cos42x-1): sin cosx x=0
xk
12/ 4sin3xcos3x+4cos3x sin3x+3 3 cos4x=3 ; 24
k k
x
13/ 2cos
22x+ cos2x=4 sin22xcos2x
14/ cos4xsinx- sin22x=4sin2(
4
x
)-7/2 với x1<3
2
x k
x k
k=0 15/ cos32x-4cos3xcos3x+cos6x-4sin3xsin3x=0
4 k
x
16/ sin3xcos3x +cos3xsin3x=sin34x
12 k
x 17/ * 8cos3(x+
3
)=cos3x ; ;
3
xk k k
18/cos10x+2cos24x+6cos3xcosx=cosx+8cosxcos23x x k 2
19/ sin 5sin
x
x=1 vô nghiệm
20 / cos7x+ sin22x= cos22x- cosx ;
8
k k
x
21/ sin
2x+ sin22x+ sin23x=3/2 ;
8
k
x m
22/ 3cos4x-2 cos23x=1
GIẢI PH ƯƠNG TRÌNH
1/ (16 2)cos x 4cosx
x k 2/cos 3 16 80
4 x x x
=1 tìm n0 xZ
21; 3
x
3/ 5cosx cos 2x+2sinx=0
xk 4/3cotx- tanx(3-8cos2x)=0
x k
5/2 sin tan 2cos
tan sin
x x
x
x x
2 2
xk 6/sin3x+cos3x+ sin3xcotx+cos3xtanx= 2sin 2x
4
xk
7/tan2xtan23xtan24x= tan2x-tan23x+tan4x
4 k
x 8/tanx+tan2x=-sin3xcos2x
3
k x k
9/sin3x=cosxcos2x(tan2x+tan2x) x k 10/ sinx sinx 1 sin2x cosx
5 ;sin
2 x k x
11/cos2 sin 2 cos2
4 x x
-1=tan
2 tan2
4
x x
2
xk
12/ cos sin 2sin 2sin
5 12 12 5
x x x x
5 5
5 ; ;
12
x k k k
GIẢI PH ƯƠNG TRÌNH
1/ sin3xcosx=1
4+ cos
3xsinx
8 k
x 2/ cosxcos2xcos4xcos8x=1/16 ; 17 17 15
k k x
3/tanx+2cot2x=sin2x x k
4/sin2x(cotx+tan2x)=4cos2x ;
2
xk k
5/ sin4x=tanx ; cos 2
x k x 6/ sin2x+2tanx=3
xk 7/ sin2x+cos2x+tanx=2
4 xk
8/tanx+2cot2x=sin2x x 4 k 9/ cotx=tanx+2cot2x
8 k x
10/a* tan2x+sin2x=3
2cotx x k ; k
b* (1+sinx)
2= cosx 2 ; 2
2
xk k