Chuyên đề 1 : Phơng trình lợng giác
1 4sin4x + 12cos2x = 7 11 2tan2x + 3tanx + 1 = 0
2 6sin23x + cos12x = 4 12 tanx – 2cotx + 1 = 0
3 3sin3x - 3 cos9x = 1 + sin33x 13 5tanx – 2cotx – 3 = 0
4 2sin2x + sinxcosx – 3cos2x = 0 14 Cos7x.cos5x- 3 sin2x=1-sin7x.sin5x
5 2 3 sin ( x + cos cos x ) x = + 3 cos 2 x 15 3sin( ) 4sin( ) 5sin(5 ) 0
6 4sin cos33x x+4cos sin 33x x+3 3 cos 4x=3 16 cos3x+sin3x+2sin2x=1
7 3sin3x +3sinxcosx + 5cos2x = 2 17 2cos2x – 3 3 sin2x – 4sin2x = -4
8 4sin3x + 3cos3x -3sinx-sin2x.cosx= 0 18 Sinx.sin2x+ sin3x = 6cos3x
4
10 8cos (3 ) cos3
3
2cos 2
x x
x
21 sin2x + sin2x – 2cos2x = 1 31 2cosxcos2x = 1+cos2x + cos3x
22 2(sin4x + cos4x) = 2sin2x – 1 32 sin42x + cos42x = 1 – 2six4x
23 sin2x – 5sinxcosx – cos2x = -2 33 3sin2x + 8sinxcosx + (8 3 - 9)cos2x = 0
24 4sin2x + 3 3 sin2x – 2cos2x = 4 34 sin2x + 2sin2x – 3 + 7cos2x = 0
25 cos3x – sin3x = cosx + sinx 35
26 sin3x + cos3x = 2(sin5x + cos5x) 36 3cos4x – sin22x + sin4x = 0
27 3sin4x + 5cos4x – 3 = 0 37 1 + sin3x + cos3x = 3
2sin2x
28 cos3x + sin3x = sin2x + sinx + cosx 38 sin3x – cos3x = 1 + sinxcosx
29 2cos3x + cos2x + sinx = 0 39 6(cosx – sinx) + sinxcosx +6 =0
30 sin2x – 12(sinx – cosx) = -12 40 2(sinx + cosx) = 4sinxcosx + 1
41 (2sinx 1)(3 os4+ c x+2sinx 4) 4 os− + c 2x=3 51 22
sin x + 2tan
2x + 5tanx + 5cotx + 4 = 0
43 Sin3x – cos3x +2(sinx+cosx) =1 53 Tan2x+cotx = 8cos2x
44 4(sin3x – cos2x) = 5(sinx – 1) 54 sin2x(cotx + tanx) = 4cos2x
45 cos3x – cos2x = 2 55 sin2x + sin23x = 3cos22x
46 sin2x – cos2x = 3sinx + cosx – 2 56 sin2x + cos2x + tanx = 2
47 cos3x – 2cos2x + cosx = 0 57 sin2x + 2cos2x = 1 + sinx – 4cosx
48 sin4
2
x
+ cos4
2
x
= 1 – 2sinx 58 2 2(sinx+c x c xos ) os = +3 cos2x
49 cos2 cos4
3
x
50 cos3x – 4cos2x + 3cosx – 4 =0 60
61 Sinx + sin2x+sin3x=1 + cosx+cos2x 71 1+ cosx + cos2x + cos3x = 0
Trang 262 tanx + cosx – cos2x = sinx(1 + tanxtan2
x
)
ĐH AN KA97
63
1 ( 1 cos cos )cos 2 sin 4
2
ĐH BK 97
ĐH Đà Nẵng KA 97
64 sin3x - sinx + sin2x = 0 74
sin cos 2(sin os ) s2
4
x + x = x c x + + co x 75 2) cos2x + 3 cosx +2 = 0ĐH Đà Nẵng 98
66
a, 3( cotgx - cosx ) - 5 (tgx - sinx) = 2
b, 1+ sin32x + cos32x =
2
3
sin4x
2cos3x = sin3x
HV KTQS 98
67 sin3x( cosx- 2sin3x) + cos3x( 1+ sinx- 2cos3x) = 0
cos3x + sin3x = k sinx cosx 1) giải phơng trình k = 2
2) Tìm k để pt có nghiệm
ĐH KTHN CS2
68
x
x
sin
5
5
sin
= 1 ĐH Mỏ ĐC 98 78 9sinx + 6cosx - 3 sin2x + cos2x = 8ĐH Ngoại thương 98
69
2sin2x - sinx.cosx - cos2x = m
1) Tìm m để pt có nghiệm
2) Tìm nghiệm khi m= 1
ĐH NN1 HN 98 79 HV QHQT 98sinx + sinx + sin2x + cosx = 1
70 cos2x + cos 4
3x
- 2 = 0 ĐH Thương mại 98
80
4
sin 2 cos 2
cos 4 tan( ) tan( )
x
+
=
81
1) cos4x + sin6x = cos2x
2) cosxcos
2
x
cos
2
3x
- sinxsin
2
x
sin
2
3x
=
2 1
ĐH Y HN 98
91 sinxsinn2x + sin3x = 6 cosĐH Y D ược TPHCM 98 3x
82
1)sin82x + cos82x = 1/8
2) (sinx + 3)sin4
2
x
- (sinx + 3)sin2
2
x
+ 1 =0 HVQY 98
92 sinĐH Lõm Nghiệp 9832xcos6x + sin6xcos32x= 3/8
83
1) cos3x + sinx - 3sin2xcosx = 0
2) sin2x + sin22x + sin23x = 3/2
3)cos4x - sin2x = cos2x
ĐH Huế 99
93 tgx + cotgx = ( sin2x + cos 2x)ĐH GTVT 99
Trang 384 Cosxcos2xcos4xcos8x = 1/16
ĐH KT QD 99 94 tgx – sin2x – cos2x +2 ( 2cosx - cosx
1
) = 0
ĐH Luật 99
85
Cho ptrình: Sinx + mcosx = 1 (1)
1)Giải pt với m = - 3
2)m= ? để mọi nghiệm của pt (1) đều
là nghiệm của pt msinx+ cosx = m2
ĐH Mỏ ĐC 99
95 sin3x + cos2x = 1 + 2 sinxcos2x 1 + sinx + cosx + tgx =0
ĐH NNgữ 99
86 Sinx + sin
2x + sin3x+ sin4x =cosx + cos2x + cos3x + cos4x ĐH NThương 99 96 1)2tgx + cotg2x = 2sin2x + 1/sin2x2)sin3x + cos3 x =2 ( sin5x + cos5 x)
3)sin2x = cos2 2x cos23x ĐH QG 99
87 (1 + sinx)2 = cosx ĐH TLợi 99 97 Sin3x cosx = 1/4 + cos3 xsinx ĐH VHúa
88
2cosx cos2x = 1+ cos2x + cos3x
4cos2 x - cos3x = acosx ( 4- a ) ( 1 +
cos2x) Tỡm a để 2 pt tương đương
ĐHY TPHCM 99
98 2( cotg2x – cotg3x ) = tg2x + cotg3xsin23x – sin22x – sin2x = 0
ĐH Y HN 99
89 Cos2x -
3sin2x - 3sinx cosx + 4
= 0
HVKTQS 99
99 Sin6 x + cos6 x = cos4x HVNH 99
90 cosHVQHQT 992x + cos22x +cos2 3x + cos24x = 3/2 100 4 sin99 3x –1 = 3sin x- 3cos3x CĐ Hải Quan
101 3cosx + cos2x – cos3x + 1 = 2sinxsin2xcosx – cos2x + cos3x = 0 CĐSP
TPHCM 99 111 3 - 4 cosĐH Cần Thơ 992x = sin x (2 sinx +1)
102 (1 2sin ).cos 3
(1 2sin )(1 sin )
-= + - KA 2009 112 sinx+cos sin 2x x+ 3 cos3x=2(cos 4x+sin )3x
KA 2009
103 cos 2x+ (1 2cos )(sin+ x x- cos )x = 0
DB KB - 2006 113 4sin3x+ 4sin2 x+ 3sin 2x+ 6cosx=0
DB KD 2006
104 (2sin2x- 1) tan 22 x+ 3(cos2x- 1)=0
6
105 cos3 osxc 3x- sin3xsin 3x=2 3 2+8
DB KA 06
3
x
-DB KA 05
106
3
2 2 os ( ) 3 os sinx=0
4
c x p c x
KA 05
116
DB KB 2007
107 2sin2x+2 3 sin cosx x+ =1 3(sinx+ 3 os )c x
2sinx sin 2
x
DBKA 2007
108 sin 3x- 3 osc x=2sin 2x ĐH
KABC-2008 118 2sin (1x + cos2 ) sin 2x + x= +1 2cosx
ĐH KD 2008
Trang 4109 sin3x- 3cos3x=sin osx c x2 - 3 sin cos2x x
3
2
x x
p p
-ĐHKA 2008
110 2sin 22 x+ sin 7x- 1 sin= x
2007
121 (1 sin )cos+ 2x x+ +(1 cos )sinx 1 sin 22x = + x
2
c x
ĐH KA 2003
122
2
c otx t anx 4sin 2
sin 2
x
x
KB2003
129 sin (2 2 4) tan2 os2 2 0
x c
p
KD2003
123
os3 sin 3
1 2sin 2
c x x
+
+
ĐH KA 2002
130 sin 32 x- cos 42 x=sin 52 x c- os 62 x
ĐH KB 2002
124 Tìm xÎ [0;14] là nghiệm của phương
trình cos3x- 4cos2x +3cosx – 4 =0
ĐH KD 2002
131 cos 3 os22 x c x c- os2x= ĐH KA 20050
KB2004 132 (2cosx- 1)(2sinx+ cos )x =sin 2x- sinx
ĐH KD 2004
126 1+ sinx + cosx+sin2x + cos2x = 0 ĐH KB 2005 133 4 4
3
os sin os( )sin(3 ) 0
c x x c x p x p
ĐH KD 2005
127
2(cos sin ) sin x cos
0
2 2sinx
=
ĐH KA 2006
134 c otx sin (1 tan x.tan )2 4
x x
ĐH KA 2006
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