Bài tập phương trình lượng giác luyện thi đh

CHUYÊN ĐỀ: PHƯƠNG
GIẢI CÁC PHƯƠNG TRÌNH SAU:
1/ 3sin22x + 7cos2x -3=0
2/ 6cos2x + 5sinx -7=0
3/ cos2x - 5sinx-3 = 0
4/ cos2x + cosx + 1= 0
5/ 7tanx - 4cotx = 12
6/ 4tan4x + 12tan2x = 7
...................................................................................
7/ 4sinx - 3cosx = 5
8/ 2cos2x + 3sin2x = 3
...................................................................................
9/ sin2x - 2sinxcosx - 3cos2x = 0
10/ sin2x - 2sin2x = 2cos2x
11/ 6sin2x + sinxcosx -cos2x = 2
..................................................................................
12/ 2sin3x + 4cos3x = 3sinx
13/ sinxsin7x = sin3xsin5x
14/ cosxcos3x - sin2xsin6x - sin4xsin6x = 0
15/ cosx + cos3x + 2cos5x = 0
16/ co22x + 3cos18x + 3co14x + co10x = 0
.................................................................................
17/ sin 2 x + sin 2 2 x + sin 2 3 x = 3 / 2
18/ cos 2 x + cos 2 2 x + cos 2 3 x + cos 2 4 x = 2
19/ sin4x+ cos4x = cos4x
20/ sin2xtan2x + cos2xcotx-sin2x = 1+tanx + cotx
21/(2sinx - 1)(2sin2x + 1)= 3 - 4cos2x
3

22/ 3sin 3 x − 3 cos 9 x = 1 + sin x
23/ 2 2(sin x + cos x ) cos x = 3 + cos 2 x

24/ 3sin( x −

π

π

π

) + 4sin( x + ) + 5sin(5 x + ) = 0
3
6
6
3
3
25/ 4 sin x cos 3 x + 4 cos x sin 3 x + 3 3 cos 4 x = 3
1
26/ 3 sin x + cos x =
cos x

..................................................................................
27/ 2(sin x + cos x) − sin x cos x = 1
28/ cos x +

1
1
1
+ sin x +
=
cos x
sin x 3

29/sin23x - cos24x = sin25x - cos26x
30/ Tìm nghiệm thuộc khoảng (0; 2π ) của PT:

5(s inx+

cos3x+sin3x
) = cos 2 x + 3
1+2sin2x

31/ Tìm x thuộc đoạn [0;14]nghiệm đúng PT:
cos3x - 4cos2x + 3cosx - 4 = 0

sin 4 x + cos 4 x 1
1
= cot 2 x −
5sin 2 x
2
8sin 2 x
2
(2 − sin 2 x)sin 3 x
33/ tan 4 x + 1 =
cos 4 x
32/

34/ tanx+cosx-cos2x= sinx(1+tanxtanx/2)
35/

2 sin x + cos x + 1 1
=

sin x − 2 cos x + 3 3

TRÌNH LƯỢNG GIÁC.
1
= sin x
8cos 2 x
cos 2 x
1
37/ cot x − 1 =
+ sin 2 x − sin 2 x
1 + tan x
2

36/

38/ 3- tanx(tanx+2sinx)+6cosx=0
39/ cos2x+cosx(2tan2x-1) = 2
40/ cotx-tanx+4sin2x=2/sin2x
41/ 3cos4x - 8cos6x + 2cos2x + 3 = 0
42/
43/
44/
45/
46/

x π
(2 − 3) cos x − 2 sin 2 ( − )
2 4 =1
2 cos x − 1
x π

x
sin 2 ( − ) tan 2 x − cos 2 = 0
2 4
2
2
cos x(cos x − 1)
= 2(1 + sin x)
sin x + cos x
2 cos 4 x
cot x = tan x +
sin 2 x
(1 − 2 sin x) cos x
= 3
(1 + 2sin x)(1 − sin x)

47/ sin x + cos x sin 2 x + 3 cos 3 x = 2(cos 4 x + sin 3 x)

3 cos 5 x − 2sin 3 x cos 2 x − sin x = 0
49/ (1 + 2sin x) 2 cos x = 1 + sin x + cos x
1
1
7π
50/
+
= 4sin(
− x)
sin x sin( x − 3π / 2)
4
48/