[r]
(1)Tài liệu ụn thi HSG - Đại Học Chuyên đề : Phơng trình lợng giác
1 4sin4x + 12cos2x = 11 2tan2x + 3tanx + = 2 6sin23x + cos12x = 12 tanx – 2cotx + = 3 3sin3x - 3cos9x = + sin33x 13 5tanx – 2cotx – = 4 2sin2x + sinxcosx – 3cos2x = 14 Cos7x.cos5x- 3sin2x=1-sin7x.sin5x 5 2 sin( x+cos cosx) x= +3 cos 2x 15 3sin( ) 4sin( ) 5sin(5 )
3 6
x- p + x+p + x+p = 6 4sin cos33x x+4cos sin 33x x+3 cos 4x=3 16 cos3x+sin3x+2sin2x=1
7 3sin3x +3sinxcosx + 5cos2x = 17 2cos2x – 3 3sin2x – 4sin2x = -4 8 4sin3x + 3cos3x -3sinx-sin2x.cosx= 18 Sinx.sin2x+ sin3x = 6cos3x
9 1+3sin2x = 2tanx 19 2 sin (3 ) 2sin
4
x+p = x
10 8cos (3 ) cos3
3
x+p = x 20 6sin 2 cos3 5sin cos
2cos
x x
x x
x
- =
21 sin2x + sin2x – 2cos2x = 31 2cosxcos2x = 1+cos2x + cos3x
22 2(sin4x + cos4x) = 2sin2x – 32 sin42x + cos42x = – 2six4x 23 sin2x – 5sinxcosx – cos2x = -2 33 3sin2x + 8sinxcosx + (8 3 - 9)cos2x = 24 4sin2x + 3 3sin2x – 2cos2x = 34 sin2x + 2sin2x – + 7cos2x = 25 cos3x – sin3x = cosx + sinx 35
26 sin3x + cos3x = 2(sin5x + cos5x) 36 3cos4x – sin22x + sin4x = 27 3sin4x + 5cos4x – = 37 1 + sin3x + cos3x = 3
2sin2x
28 cos3x + sin3x = sin2x + sinx + cosx 38 sin3x – cos3x = + sinxcosx 29 2cos3x + cos2x + sinx = 39 6(cosx – sinx) + sinxcosx +6 =0 30 sin2x – 12(sinx – cosx) = -12 40 2(sinx + cosx) = 4sinxcosx +
41 (2sinx 1)(3 os4c x 2sinx 4) osc 2x 3
51 22
sin x + 2tan
2x + 5tanx + 5cotx + =
42 cos sin 10
cos sin
x x
x x
+ + + = 52 Sinx - cosx +7sin2x=1
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 = 55 sin2x + sin23x = 3cos22x 46 sin2x – cos2x = 3sinx + cosx – 56 sin2x + cos2x + tanx =
47 cos3x – 2cos2x + cosx = 57 sin2x + 2cos2x = + sinx – 4cosx
48 sin4
2 x
+ cos4
2 x
= – 2sinx 58 2(sinxc x c xos ) os 3 cos2x 49 cos2 cos4
3 x
x= 59 2cos2 3cos4
5
x x
+ =
50 cos3x – 4cos2x + 3cosx – =0 60
61 Sinx + sin2x+sin3x=1 + cosx+cos2x 71 1+ cosx + cos2x + cos3x =
62 tanx + cosx – cos2x = sinx(1 + tanxtan 72
( )2
cos 2x- cos 4x = +6 2sin 3x §H AN KA97
(2)Tài liệu ôn thi HSG - Đại Học
2 x )
63
1 ( cos cos )cos 2 sin 4
2
x x x x
- + =
§H BK 97
73 sin 3x+2cos 2x=2
ĐH Đà Nẵng KA 97
64 sin3x - sinx + sin2x = 0 74 65 sin8 cos8 2(sin10 os )10 5 s2
4
x+ x= x c x+ + co x 75 2) cos2x + cosx +2 =
ĐH Đà Nẵng 98
66
a, 3( cotgx - cosx ) - (tgx - sinx) = b, 1+ sin32x + cos32x =
2
sin4x §H GTVT 97- 98
76 2cos3x = sin3x
HV KTQS 98
67 sin3x( cosx- 2sin3x) + cos3x( 1+ sinx- 2cos3x) = 0
§H KiÕn Tróc HN 98
77
cos3x + sin3x = k sinx cosx
1) gi¶i phơng trình k =
2) Tìm k để pt có nghiệm
§H KTHN CS2
68
x x
sin
5 sin
= §H Má §C 98 78
9sinx + 6cosx - sin2x + cos2x = ĐH Ngoại thương 98
69
2sin2x - sinx.cosx - cos2x = m 1) Tìm m để pt có nghiệm 2) Tìm nghiệm m= ĐH NN1 HN 98
79 sinx + sinx + sin2x + cosx =
HV QHQT 98
70 cos2x + cos 4
3x
- = ĐH Thương mại 98
80
4
4
sin cos
cos tan( ) tan( )
4
x x
x
x x
p p
+ =
- + ĐHXD 98
81
1) cos4x + sin6x = cos2x
2) cosxcos
x
cos 3x
- sinxsin
x
sin
3x
= ĐH Y HN 98
91 sinxsinn2x + sin3x = cos3x
ĐH Y D ược TPHCM 98
82
1)sin82x + cos82x = 1/8
2) (sinx + 3)sin4
2
x
- (sinx + 3)sin2
2
x
+ =0 HVQY 98
92 sin32xcos6x + sin6xcos32x= 3/8
ĐH Lâm Nghiệp 98
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
84 Cosxcos2xcos4xcos8x = 1/16
ĐH KT QD 99 94
tgx – sin2x – cos2x +2 ( 2cosx -
x
cos
) = ĐH Luật 99
(3)Tài liệu ôn thi HSG - Đại Học
85
Cho ptr×nh: Sinx + mcosx = (1) 1)Gi¶i pt víi m = -
2)m= ? để nghiệm pt (1) nghiệm pt msinx+ cosx = m2
ĐH Mỏ ĐC 99
95
sin3x + cos2x = + sinxcos2x + sinx + cosx + tgx =0
ĐH NNgữ 99
86
Sinx + sin2x + sin3x+ sin4x =cosx +
cos2x + cos3x + cos4x ĐH NThương 99 96
1)2tgx + cotg2x = 2sin2x + 1/sin2x 2)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 VHóa
88
2cosx cos2x = 1+ cos2x + cos3x 4cos2 x - cos3x = acosx ( 4- a ) ( +
cos2x) Tìm a để pt tương đương ĐHY TPHCM 99
98
2( cotg2x – cotg3x ) = tg2x + cotg3x sin23x – sin22x – sin2x = 0
ĐH Y HN 99
89
Cos2x - 3sin2x - 3sinx cosx +
=
HVKTQS 99
99 Sin6 x + cos6 x = cos4x HVNH 99
90 cos2x + cos22x +cos2 3x + cos24x = 3/2
HVQHQT 99 100
4 sin3x –1 = 3sin x- 3cos3x CĐ Hải Quan
99
101
3cosx + cos2x – cos3x + = 2sinxsin2x cosx – cos2x + cos3x = CĐSP TPHCM 99
111 - cos2x = sin x (2 sinx +1)
ĐH Cần Thơ 99
102 (1 2sin ).cos
(1 2sin )(1 sin )
x x
x x
- =
+ - KA 2009 112
3
sinx+cos sin 2x x+ cos3x=2(cos 4x+sin )x
KA 2009
103 cos 2x+ +(1 cos )(sinx x- cos )x =0
DB KB - 2006 113
3
4sin x+4sin x+3sin 2x+6 cosx=0
DB KD 2006
104
2 2
(2sin x- 1) tan 2x+3(cos x- 1)=0
DB KB 2006 114 2sin(2x 6) 4sinx
p
- + + = DB KA 2006
105 3
2 cos3 os sin sin
8
xc x- x x= +
DB KA 06
115
2
4sin os2 os ( )
2
x
c x c x p
- = +
-DB KA 05
106
3
2 os ( ) os sinx=0
c x- p - c x- DB KA 05
116
5
sin( ) os( ) os
2 4
x x x
c c
p p
- - - =
DB KB 2007
107
2
2sin x+2 sin cosx x+ =1 3(sinx+ os )c x
DB KA 2007 117
1
sin sinx 2cot
2sinx sin
x x
x
+ - - =
DBKA 2007
108 sin 3x- osc x=2sin 2x ĐH
KABC-2008 118
2sin (1x +cos2 ) sin 2x + x= +1 cosx
ĐH KD 2008
109 sin3x- 3cos3x=sin osx c x2 - sin cos2x x
ĐH KB 2008 119
1
4sin( )
sinx sin( )
2
x x
p p
+ =
-ĐHKA 2008
110 2sin 22 x+sin 7x- =1 sinx
ĐH KB 2007 120
2
(sin os ) cos
2
x x
c x
+ + = ĐH KD
2007
(4)Tài liệu ôn thi HSG - Đại Học
121
2
(1 sin )cos+ x x+ +(1 cos )sinx sin 2x = + x
ĐH KA 2007 128
2
os2
c otx sin sin
1 t anx
c x
x x
- = +
-+
ĐH KA 2003
122
2 c otx t anx 4sin
sin x
x
- + = ĐH
KB2003
129
2 2
sin ( ) tan os
2
x x
x c p
- - = ĐH
KD2003
123
os3 sin
5(sinx ) os2
1 2sin
c x x
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 xỴ [0;14] nghiệm phương trình cos3x- 4cos2x +3cosx – =0 ĐH KD 2002
131 cos os22 x c x c- os2x=0 ĐH KA 2005
125
2
5sin x-2=3(1-sinx) tan x ĐH
KB2004 132
(2cosx- 1)(2sinx+cos )x =sin 2x- sinx
ĐH KD 2004
126 1+ sinx + cosx+sin2x + cos2x =
ĐH KB 2005 133
4
os sin os( )sin(3 )
4
c x+ x c+ x- p x- p - =
ĐH KD 2005
127
6
2(cos sin ) sin x cos 2sinx
x+ x - x=
ĐH KA 2006
134 c otx sin (1 tan x.tan )2
x x
+ + =
ĐH KA 2006
Chúc em sớm hoàn thành tập !