[r]
Trang 1Phơng trình lợng giác-PDT
1/ Tìm x (0; 2) của pt :
5(sin x + cos 3 x +sin 3 x
1+2sin 2 x )=cos 2 x +3
2/ sin23x - cos24x = sin25x - cos26x
3/ Tìm x [0;14] : cos3x - 4cos2x + 3cosx - 4 = 0 4/ cosx+ cos2x + cos3x + cos4x + cos5x = -1/2
5/.(cos2x - 1)(sin2x + cosx + sinx) = sin22x 6/.5sinx - 2 = 3(1 - sinx)tg2x
7/.cotgx - 1 = cos 2 x
1+tgx + sin2x -
1
2 sin2x 8/.cotgx - tgx + 4sin2x =
2
sin 2 x
9/ sin2(2x −
π
4)tg2x −cos2x
x x x x
10/. (2 cos x −1)(2 sin x+cos x)=sin 2 x −sin x 12/ cos23xcos2x - cos2x = 0
13/ 1 + sinx + cosx + sin2x + cos2x = 0 14/ cos3x + cos2x - cosx - 1 = 0
15/
0
2 2sin
x
16/.cotx + sinx(1+tanx.tanx/2) = 4
17/.1 sin 2xcosx1 cos 2xsinx 1 sin 2x 18/ 2sin22x + sin7x - 1 = sinx
19/
2
x x
x
20/.Tìm m: 4(sin4x +cos4x)+cos 4 x +2 sin 2 x −m=0
có ít nhất một nghiệm thuộc đoạn [0; π
2] 21/ sin4x +cos4x
5 sin2 x =
1
2cot g 2 x −
1
4
x +1=(2 −sin
2
2 x)sin 3 x
cos4x
23/ tgx + cosx - cos2x = sinx(1 + tgxtgx/2)
24/ √8 cos12x=sin x 25/.
cot gx=tgx+2 cos4 x
sin2 x
26/ 3 − tgx( tgx+2 sin x )+6 cos x =0 27/ cos2x + cosx(2tg2x - 1) = 2 29/ sin(cosx) = 1 30/ 3 cos 4 x − 9cos6x+2 cos2x +3=0 31/. tg 2 x − tgx=1
3cos x sin 3 x 32/.
sin 3 x
sin 5 x
5
33/
(sin x+cos x)3−√2(sin 2 x +1)+sin x +cos x −√2=0
34/ √1+sin x +cos x =0 35/
sin 2 x +4(cos x − sin x)=4
36/.Cho PT: 2 sin x+cos x+1
sin x − 2cos x +3=a (2) (a là tham số)
a) Giải a =1/3 b) Tìm a để phơng trình (2) có nghiệm ?
37/.Cho phơng trình: cos 2 x+(2m −1) cos x+1− m=0
1) Giải m = 1 2) m=? để PT có nghiệm/ (π2;π)
38/ (2−√3)cos x −2 sin2
(2x −
π
4)
39/
cos2x (cos x −1)
sin x+cos x =2 (1+sin x )
40/ 2 cos 2 x −8 cos x +7= 1
cos x 41/.
2 sin3x +cos 2 x − cos x=0
42/.Cho phơng trình: (3+2 √2)tgx+(3− 2 √2)tgx=m
1) Giải m = 6 2) m=? để PT có đúng 2 ng PB/
(− π
2;
π
2)
43/ 4 sin22 x +6 sin2x − 9 −3 cos 2 x
tgx+cot g 2 x=
√2(cos x −sin x ) cot gx − 1
44/ sin2x+sin22 x+sin23 x=2 45/
sin x cos 4 x +cos 2 x sin 3 x=0
46/ 1+sin x+cos x+sin2 x +cos 2 x=0 47/.tg2x + cotgx = 8cos 2 x
48/ sin6x+cos6x
cos2x − sin2x =
13
8 tg 2 x 49/.
50/ sinx.cosx + cosx = -2sin2x - sinx + 1 51/ sin3x = cosx.cos2x.(tg2x + tg2x) 52/ cos x (cos x+2sin x )+3 sin x(sin x+ √2)
Trang 2sin x+sin y=1
x2− πx
2 =y
2
− πy
2
¿
cos4 x
3 =cos
2
(x3)
54/
sin x+sin2 x +sin 3 x −√3 (cos x +cos 2 x+cos 3 x)=0 55/ (1− √sin x)−cos 2 x=2√sin x sin
2
x − 1
56/ sin3
(x + π
4)=√2 sin x 57/
1
tgx+cot g 2 x=
√2(cos x −sin x ) cot gx − 1
58/ GBL: 2m(cosx + sinx) = 2m2 + cosx - sinx + 3/2 59/ sin2000x +cos2000x=1
60/ sin(103 π −
x
2)=1
2sin(10π +
3 x
2 ) 61/
√1 −sin 2 x+√1+sin 2 x
62/ cos2x + cos4x + cos6x = cosxcos2xcos3x + 2 63/ cosx + cos2x + cos3x + cos4x = 0
64/ sin 4 x + cos2x + 4cos 6 x = 0
65/ sinx + sin 2 x + sin 3 x + sin 4 x = cosx + cos 2 x + cos 3 x + cos 4 x
66/.sin 3 x.cos3x + cos 3 x.sin3x = sin 3 4x 67/ 2tgx + cotg2x = 2sin2x + 1/sin2x
68/ cosx.sinx + |cos x +sin x|=1
69/.cos7x - √3 sin7 x=−√2 tm: 2
5π < x<
6
7π 70/.9sinx + 6cosx - 3sin2x + cos2x = 8 71/ 3(cotgx - cosx) - 5(tgx - sinx) = 2
72/. ( √1− cos x+√cos x) cos 2 x=1
2sin 4 x 73/ tgx +
2cotg2x = sin2x 74/.2cosxcos2x = 1 + cos2x + cos3x 75/ 3sinx + 2cosx = 2 + 3tgx 76/ sin 3 x.cos3x + cos 3 x.sin3x = sin 3 4x
77/ (3 x − π
4)=sin 2 x sin(x+ π
4)
sin x+sin2 x +sin 3 x
cos x +cos2 x+cos3 x=√3
78/.T×m nghiÖm: sinxcos4x + 2sin 2 2x = 1 - 4 sin2
(π4−
x
2) tm :
¿
|x −1|<3
x2+3>− x
¿
79/.(1 + tgx)(1 + sin2x) = 1 + tgx 80/.2sin3x - sinx = 2cos3x - cosx + cos2x
81/.sinx + cosx + cos2x - 2sinx.cosx = 0