CHUYÊN ĐỀ:
PHƯƠNG TRÌNH LƯỢNG GIÁC
.
GIẢI CÁC PHƯƠNG TRÌNH SAU:
1/ 3sin
2
2x + 7cos2x -3=0
2/ 6cos
2
x + 5sinx -7=0
3/ cos2x - 5sinx-3 = 0
4/ cos2x + cosx + 1= 0
5/ 7tanx - 4cotx = 12
6/ 4tan
4
x + 12tan
2
x = 7
7/ 4sinx - 3cosx = 5
8/ 2cos2x + 3sin2x = 3
9/ sin
2
x - 2sinxcosx - 3cos
2
x = 0
10/ sin2x - 2sin
2
x = 2cos2x
11/ 6sin
2
x + sinxcosx -cos
2
x = 2
12/ 2sin
3
x + 4cos
3
x = 3sinx
13/ sinxsin7x = sin3xsin5x
14/ cosxcos3x - sin2xsin6x - sin4xsin6x = 0
15/ cosx + cos3x + 2cos5x = 0
16/ co22x + 3cos18x + 3co14x + co10x = 0
17/
2 2 2
sin sin 2 sin 3 3/ 2
x x x+ + =
18/
2 2 2 2
cos cos 2 cos 3 cos 4 2
x x x x
+ + + =
19/ sin
4
x+ cos
4
x = cos4x
20/ sin
2
xtan2x + cos
2
xcotx-sin2x = 1+tanx + cotx
21/(2sinx - 1)(2sin2x + 1)= 3 - 4cos
2
x
22/
3
3sin3 3 cos9 1 sin
x x x
− = +
23/
2 2(sin cos )cos 3 cos 2
x x x x
+ = +
24/
3sin( ) 4sin( ) 5sin(5 ) 0
3 6 6
x x x
π π π
− + + + + =
25/
3 3
4sin cos3 4cos sin 3 3 3 cos 4 3
x x x x x
+ + =
26/
1
3 sin cos
cos
x x
x
+ =
27/
2(sin cos ) sin cos 1
x x x x
+ − =
28/
1 1 1
cos sin
cos sin 3
x x
x x
+ + + =
29/sin
2
3x - cos
2
4x = sin
2
5x - cos
2
6x
30/ Tìm nghiệm thuộc khoảng
(0;2 )
π
của PT:
cos3x+sin3x
5(sinx+ ) cos2 3
1+2sin2x
x
= +
31/ Tìm x thuộc đoạn [0;14]nghiệm đúng PT:
cos3x - 4cos2x + 3cosx - 4 = 0
32/
4 4
sin cos 1 1
cot 2
5sin 2 2 8sin 2
x x
x
x x
+
= −
33/
2
4
4
(2 sin 2 )sin 3
tan 1
cos
x x
x
x
−
+ =
34/ tanx+cosx-cos
2
x= sinx(1+tanxtanx/2)
35/
2sin cos 1 1
sin 2cos 3 3
x x
x x
+ +
=
− +
36/
2
1
sin
8cos
x
x
=
37/
2
cos 2 1
cot 1 sin sin 2
1 tan 2
x
x x x
x
− = + −
+
38/ 3- tanx(tanx+2sinx)+6cosx=0
39/ cos2x+cosx(2tan
2
x-1) = 2
40/ cotx-tanx+4sin2x=2/sin2x
41/ 3cos4x - 8cos
6
x + 2cos
2
x + 3 = 0
42/
2
(2 3)cos 2sin ( )
2 4
1
2cos 1
x
x
x
π
− − −
=
−
43/
2 2 2
sin ( )tan cos 0
2 4 2
x x
x
π
− − =
44/
2
cos (cos 1)
2(1 sin )
sin cos
x x
x
x x
−
= +
+
45/
2cos 4
cot tan
sin 2
x
x x
x
= +
46/
(1 2sin )cos
3
(1 2sin )(1 sin )
x x
x x
−
=
+ −
47/
3
sin cos sin 2 3 cos3 2(cos4 sin )
x x x x x x
+ + = +
48/
3 cos5 2sin 3 cos 2 sin 0
x x x x
− − =
49/
2
(1 2sin ) cos 1 sin cos
x x x x
+ = + +
50/
1 1 7
4sin( )
sin sin( 3 / 2) 4
x
x x
π
π
+ = −
−