PTLG TRONG CAC DE THI ĐH 2002-2010

PHƯƠNG TRÌNH LƯƠNG GIÁC TRONG CÁC ĐỀ THI ĐẠI HỌC
1. (1 + sin
2
x)cosx + (1 + cos
2
x)sinx = 1 + sin2x 2. 2sin
2
2x + sin7x – 1 = sinx
3.
x x
2
(sin cos ) 3 cos x 2
2 2
+ + =
4.
1 1
sin 2x sin x 2cot 2x
2sin x sin 2x
+ − − =
5.
2
2cos x+2 3sinxcosx+1=3(sinx+ 3cosx)
6.
5x x 3x
sin( ) cos( ) 2 cos
2 4 2 4 2
π π
− − − =
7.
sin 2x cos2x
tan x cot x

cos x sin x
+ = −
8.
2 2 sin(x )cos x 1
12
π
− =
9. (1 – tanx)(1 + sin2x) = 1+ tanx 10.
1 1 7
4sin( x)
3
sin x 4
sin(x )
2
π
+ = −
π
−
11.
3 3 2 2
sin x 3 cos x sin x cos x 3sin x cos x− = −
12. 2sinx(1 + cos2x) + sin2x = 1 + 2cosx 13. tanx = cotx + 4cos
2
2x
14.
2
sin(2x ) sin(x )
4 4 2
π π
− = − +

15.
1
2sin(x ) sin(2x )
3 6 2
π π
+ − − =
16. 3sinx + cos2x+sin2x=4sinxcos
2
x
2
17. 4(sin
4
x + cos
4
x) + cos4x + sin2x = 0
18.
(1 2sin x)cos x
3
(1 2sin x)(1 sin x)
−
=
+ −
19.
3
cos5x – 2sin3xcos2x – sinx = 0
20. sinx + cosxsin2x +
3
cos3x = 2(cos4x + sin
3
x)

21.
(1 sinx cos2x)sin(x )
1
4
cos x
1 t anx
2
π
+ + +
=
+
22. (sin2x + cos2x)cosx + 2 cos2x – sinx = 0
23. sin2x – cos2x + 3sinx – cosx – 1 = 0 24.
3 3
2 3 2
cos3x cos x sin 3x sin x
8
+
− =
25. 2sin(2x –
6
π
) + 4sinx + 1 = 0 26. cos2x + (1 + 2cosx)(sinx – cosx) = 0
27. (2sin
2
x – 1)tan
2
2x + 3(2cos
2
x – 1) = 0 28. 4sin

3
x + 4sin
2
x + 3sin2x + 6cosx = 0.
29. cos
3
x + sin
3
x + 2sin
2
x = - 1 30.
6 6
2(cos x sin x) sin x cos x
0
2 2sin x
+ −
=
−
31.
x
cot x sinx(1 tan x tan ) 4
2
+ + =
32. cos3x + cos2x – cosx - 1 =0
Bài tập thêm
1.
2
17
sin(2 ) 16 2 3.sin cos 20sin ( )
2 2 12

+ + = + +
x
x x x
π π

2.
2 sin
4
(1 sin 2 ) 1 tan
cos
 
−
 ÷
 
+ = +
π
x
x x
x
3.
1 1
sin 2 sin 2cot 2
2sin sin 2
+ − − =x x x
x x
4.sin .tan 2 3(sin 3 tan 2 ) 3 3+ − =x x x x 5.
cos2 5 2(2 cos )(sin cos )+ = − −x x x x
voxuantruong.ht
6.
3 3

sin .(1 cot ) cos (1 tan ) 2sin 2+ + + =x x x x x
7.
3 3
sin .sin 3 cos cos3 1
8
tan tan
6 3
+
= −
   
− +
 ÷  ÷
   
π π
x x x x
x x
8.
2 2
1 sin sin cos sin 2cos
2 2 4 2
 
+ − = −
 ÷
 
x x x
x x
π
9.
3
3

2
cos cos3 sin sin 3
4
+ =
x x x x
10.
2 2 3 3
tan tan .sin cos 1 0− + − =x x x
11.
2 2
1 8 1
2cos cos ( ) sin 2 3cos( ) sin
3 3 2 3
+ + = + + + +
π
π
x x x x x
12.9sinx + 6cosx – 3sin2x + cos2x = 8 13.
     
π π
π − − − = +
 ÷  ÷  ÷
     
2
3
cos x-
4
2
x
4sin 3 sin 2x 1 2

2 2
14.
− = −
2 2 2 2
sin 3x cos 4x sin 5x cos 6x
15.
   
+ + − + =
 ÷  ÷
   
π π
x x x x
3
2 2 cos 2 sin 2 cos 4sin 0
4 4
16.9sinx + 6cosx – 3sin2x + cos2x = 8 17.
6 6
2 2
sin cos 1
tan 2
cos sin 4
+
=
−
x x
x
x x
18.tan(
5
2

π
-x) +
sinx
1 + cosx
= 2 19.2cos3x +
3
sinx + cosx = 0
20.cos
2
3xcos2x – cos
2
x = 0. 21.
sin 2 2 2(sinx+cosx)=5
−
x
voxuantruong.ht