PHƯƠNG TRÌNH LƯỢNG
GIÁC
1) sin2x+sin 32 x=cos 22 x+cos 42 x
2) sin2 2cos 0
1 sin
+
2 2cos cosx sinx x 4
p
æ ö÷
- = ççè + ÷ø
4) (2sin2x- 1)tan 22 x+3(2cos2x- 1)=0
5) 8cos cos33x x+8sin3xsin3x=1
1 cos
x x
x
+
sin cos4 sin 2 4sin
4 2 2
x
x x- x= æçççèp- ö÷÷÷ø
-8) sin6x+cos6x=2(sin8x+cos )8x
9) cos cos2 cos4 cos8 1
16
10) sin2 (cotx x+tan2 )x =4cos2x
11) 2tan cot2 2sin2 1
sin2
x
12) sin2x+sin 22 x+sin 32 x=2
13) cos3 tan5x x=sin7x
14)
sin cos 1(tan cot2 )
x
15) sin3x+cos3x=2(sin5x+cos )5x
16)
2
cos (cos 1) 2(1 sin )
sin cos
+
17) tan2 1 cos
1 sin
x x
x
+
=
-18)
2 4
4
(2 sin 2 )sin3 tan 1
cos
x
x
-+ =
19) 2 2sin 1 1
4 sin cos
x
p
æ ö÷
ç + ÷= +
çè ø
20) 2tan cot2 3
sin2
x
3tan3 cot2 2tan
sin4
x
22) 3(sin tan ) 2(1 cos ) 0 tan sin
24)
2
cos (2sin 3 2) 2cos 1
1
1 sin2
x
-= +
cos cos cos sin sin sin
26) 4cos3x+3 2sin2x=8cosx
27) sin2 (cotx x+tan2 )x =4cos2x
28) tan3 tan 1
4
æ ö÷
ç - ÷=
çè ø sin4x=tanx
29) sin (2cos 3 2) 2sin2 1 1
1 sin2
x
cosx+sin2x =sin4x
4
x+ æçççèx- pö÷÷÷ø=
cot tan
sin2
x
x
33) 4sin3x+4sin2x+3sin2x+6cosx=0
34) tan cos sin2 0
2
x
x+ x=
35) 1 3tan+ x=2sin2x
36) cotx=tanx+2tan2x
37) 2cos23 1 3cos4
38) 3cos4x- 2cos 32 x=1
39) cos2x+cos (tanx 2x- 1)=2
40)
sin cos2x x+cos (tanx x- 1) 2sin+ x=0
41) cos 3 cos22 x x- cos2x=0 [ĐH-khối A-2005]
42) cos4 sin4 cos .sin 3 3 0
x+ x+ æçççèx- pö÷÷÷ø æçççèx- pö÷÷÷ø- = [ĐH-khối D-2005]
43) 5sinx- 2=3(1 sin )tan- x 2x [ĐH-khối B-2004]
Trang 244)
2(sin cos ) sin cos 0
2 2sin
x
cot tan 4sin2
sin2
x
46) (1 sin cos2 )sin 1
x x
p
æ ö÷
+ + ççè + ÷ø=
+
[ĐH-khối A-2010]
47) (2cosx- 1)(2sinx+cos )x =sin2x- sinx [ĐH-khối D-2004]
48) 2sin 22 x+sin7x- 1 sin= x [ĐH-khối B-2007]
49) sin 32 x- cos 42 x=sin 52 x- cos 62 x [ĐH-khối B-2002]
50) sinx+cosx+ +1 sin2x+cos2x=0 [ĐH-khối B-2005]
51) sin2 tan2 cos2 0
æ ö÷
52) cot sin 1 tan tan 4
2
x
x+ xæçççè + x ö÷÷÷ø= [ĐH-khối D-2005]
x x
x
p
æ ö÷
54) cos3x+cos2x- cosx- 1 0= [ĐH-khối D-2006]
55) cos3x- 4cos2x+3cosx- 4=0 [ĐH-khối D-2002]
56) cot sin 1 tan tan 4
2
x
x+ xæçççè + x ö÷÷÷ø= [ĐH-khối B-2006]
57)
2
x x
x
p p
æ ö÷
+ æç ö÷= ççè - ø÷
÷
çè ø
[ĐH-khối A-2008]
58) 12) 2sin (1 cos2 )x + x +sin2x= +1 2cosx [ĐH-khối D-2008]
59) 13) (1 2sin ) cos+ x2 x= +1 sinx+cosx [CĐ-khối A,B,D-2009]
60) 3sin3x- 3cos9x= +1 4sin 33 x [ĐH-Mỏ địa chất Hà Nội-1995]
61) 2 2(sinx+cos )cosx x= +3 cos2x [ĐH-GTVT Hà Nội-2000]
62)
2
sin cos 3cos 2
x
x
x
64) sin3x- 3cos3x=sin cosx 2x- 3sin2xcosx [ĐH-khối B-2008]
65) sin3x- 3cos3x=2sin2x [CĐ-khối A,B,D-2008]
66) (1 2sin )cos
3 (1 2sin )(1 sin )
-=
67) sinx+cos sin2x x+ 3cos3x=2(cos4x+sin )3x [ĐH-khối B-2009]
68) 3cos5x- 2sin3 cos2x x- sinx=0 [ĐH-khối D-2009]
69) (sin2x+cos2 )cosx x+2cos2x- sinx=0 [ĐH-khối B-1010]
70) sin2x- cos2x+3sinx- cosx- 1 0= [ĐH-khốiD-2010]