Bài tập: Giải phương trình lượng giác

Gi¶i c¸c ph¬ng tr×nh lîng gi¸c sau:
1.
( )
x
1 cos x sin 0
2
π +
− π − + =
2.
1
sin xsin 2x sin 3x sin 4x
4
=
3.
2 2
2sin x 1 2sin x
4
π
 
− = −
 ÷
 
4. sin 3x sin 6x sin 9x=
5.
3 3
3
sin x cos3x sin 3x cos x
8
+ =
6.
( )

sin8x cos6x 3 sin 6x cos8x− = +
7.
3
3sin x 3 cos3x 1 4sin x+ = +
8.
( )
3
2sin x 1 cos2x sin 2x ,
4 2
trªn
π π
 
+ =
 ÷
 
9.
2
6 6
4 3sin 2x
sin x cos x sin 3x
4
−
− = +
10.
3
2cos 4x cos2x 4cos 2x 3cos 2x= −
11.
( ) ( )
0 0 2
4cos x sin 30 x cos 60 x cos 3x+ + =

12.
2
1 cos 2x 5
6cos x sin 2x
2 2
−
+ =
13.
2
x x
sin x 2cos 2x sin x cos 2x 4sin cos
2 2
− = −
14.
cos2x sin 3x sin 5x 4cos x 1
+ + = −
15.
2
2
1
2tg x 2tgx 1
cos x
+ − =
16.
tg5x tg3x=
17.
tg2xtg7x 1=
18.
( ) ( )
2

2sin x cos x 1 cos x sin x− + =
19. 1 sin x cos 2x sin x cos2x+ = +
20.
4 4
sin x cos x cos 4x+ =
21.
2 2
3sin x 2sin x cos x cos x 0− − =
22.
tg3x tgx 0− =
23. sin x sin 2x sin 3x cos x cos 2x cos3x+ + = + +
24.
2 2 2 2
sin x sin 2x sin 3x sin 4x 2+ + + =
25.
2
2cos x 1 sin 3− =
26.
3 3
sin x cos x 1 sin x cos x− = +
27.
cos3x cos 2x sin 3x
− =
28.
1 1
2sin 3x 2cos3x
sin x cos x
− = +
29.
2

cos x 2cos x 4sin x sin 2x− = −
30.
tgx tg2x tg3x 0+ + =
31. cos9x 2cos6x 2− =
32.
2
cot g2x cot gx 8cos x+ =
33.
( ) ( )
1 tgx 1 sin 2x 1 tgx+ + = +
34.
2
8cos x 3cos 4x cos 2x 4= + +
35.
2 2 2 2
tg xtg 3xtg4x tg `x tg 3x tg4x= − +
36.
3
2
3
1 cos x
tg x
1 sin x
+
=
+
37.
3 3
x x
sin cos

1
2 2
cos x
2 sin x 3
−
=
+
38.
( )
8 8 12 12
sin x cos x 32 sin x cos x+ = +
39.
2 2 2
1
sin x sin 3x sin x.sin 3x
4
+ =
40.
( )
2
cos 4x cos 2x sin x 5+ − =
NguyÔn Xu©n Thä §¹i häc khoa häc tù nhiªn
§iÖn tho¹i: 0914379466; 031.677101
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