[r]
(1)Phơng trình lợng giác-PDT 1/ Tìm x (0; 2) cña pt :
5(sinx+cos 3x+sin 3x
1+2sin 2x )=cos 2x+3
2/ sin23x - cos24x = sin25x - cos26x
3/ T×m x [0;14] : cos3x - 4cos2x + 3cosx - = 4/ cosx+ cos2x + cos3x + cos4x + cos5x = -1/2 5/.(cos2x - 1)(sin2x + cosx + sinx) = sin22x 6/.5sinx - = 3(1 - sinx)tg2x
7/.cotgx - = cos 2x
1+tgx + sin
2x -
2 sin2x 8/.cotgx - tgx + 4sin2x = sin 2x 9/ sin2(x
2− π 4)tg
2
x −cos2x
2=0 10/
4
cos sin cos sin
4
x x x x
10/ (2 cosx −1)(2 sinx+cosx)=sin 2x −sinx 12/ cos23xcos2x - cos2x = 13/ + sinx + cosx + sin2x + cos2x = 14/ cos3x + cos2x - cosx - = 15/
6
2 sin sin cos
0 2sin
cos x x x x x
16/.cotx + sinx(1+tanx.tanx/2) =
17/.
2
1 sin x cosx cos x sinx 1 sin 2x 18/ 2sin22x + sin7x - = sinx
19/
2
sin cos cos
2 x x x
20/.T×m m: 4(sin4x
+cos4x)+cos 4x+2 sin 2x m=0
có nghiệm thuộc đoạn [0;π 2] 21/ sin
4x
+cos4x
5 sin2x =
2cotg2x −
8sin 2x 22/ tg
4
x+1=(2−sin
2
2x)sin 3x cos4x
23/ tgx + cosx - cos2x = sinx(1 + tgxtgx/2)
24/ √
8 cos2x=sinx 25/ cot gx=tgx+2 cos4x
sin2x
26/ 3−tgx(tgx+2 sinx)+6 cosx=0 27/ cos2x + cosx(2tg2x - 1) = 29/ sin(cosx) =
30/ 3 cos 4x −9cos6x+2 cos2x
+3=0 31/. tg 2x −tgx=1
3cosxsin 3x 32/ sin 3x
3 =
sin 5x 33/
(sinx+cosx)3−√2(sin 2x+1)+sinx+cosx −√2=0
34/ √1+sinx+cosx=0 35/
sin 2x+4(cosx −sinx)=4
36/.Cho PT: sinx+cosx+1
sinx −2cosx+3=a (2) (a lµ tham sè)
a) Giải a =1/3 b) Tìm a để phơng trỡnh (2) cú nghim ?
37/.Cho phơng trình: cos 2x+(2m −1)cosx+1− m=0
1) Giải m = 2) m=? để PT có nghiệm/ (π
2;π) 38/ (2−√3)cosx −2 sin
2 (2x−
π 4) cosx −1 =1
39/ cos2x(cosx −1)
sinx+cosx =2(1+sinx)
40/ cos 2x −8 cosx+7=
cosx 41/ sin3x+cos 2x −cosx=0
42/.Cho phơng trình: (3+2√2)tgx+(3−2√2)tgx=m 1) Giải m = 2) m=? để PT có ng PB/
(−π 2;
π 2)
43/ sin
2x+6 sin2x −9−3 cos 2x
cosx =0
43/.A/
tgx+cotg2x=
√2(cosx −sinx)
cot gx−1 44/ sin2x+sin22x+sin23x=2 45/
sinxcos 4x+cos 2xsin 3x=0
46/ 1+sinx+cosx+sin2x+cos 2x=0 47/.tg2x + cotgx = 8cos2x
48/ sin
x+cos6x
cos2x −sin2x = 13
8 tg 2x 49/
50/ sinx.cosx + cosx = -2sin2x - sinx + 1
51/ sin3x = cosx.cos2x.(tg2x + tg2x)
52/ cosx(cosx+2sinx)+3 sinx(sinx+√2)
(2)¿ sinx+siny=1
x2−πx =y
2 −πy
2
¿{
¿
cos4x =cos
2 (x3) 54/
sinx+sin2x+sin 3x −√3(cosx+cos 2x+cos 3x)=0 55/ (1−√sinx)−cos 2x=2√sinxsin
x −1 56/ sin3(x+π
4)=√2 sinx 57/
tgx+cotg2x=
√2(cosx −sinx)
cot gx−1
58/ GBL: 2m(cosx + sinx) = 2m2 + cosx - sinx + 3/2
59/ sin2000x+cos2000x=1
60/ sin(3π 10 −
x 2)=
1 2sin(
π 10+
3x
2 ) 61/
√1−sin 2x+√1+sin 2x
sinx =4 cosx
62/ cos2x + cos4x + cos6x = cosxcos2xcos3x + 63/ cosx + cos2x + cos3x + cos4x =
64/ sin4x + cos2x + 4cos6x = 0
65/ sinx + sin2x + sin3x + sin4x = cosx + cos2x + cos3x + cos4x
66/.sin3x.cos3x + cos3x.sin3x = sin34x
67/ 2tgx + cotg2x = 2sin2x + 1/sin2x
68/ cosx.sinx + |cosx+sinx|=1
69/.cos7x - √3 sin7x=−√2 tm: 5π<x<
6 7π 70/.9sinx + 6cosx - 3sin2x + cos2x = 71/ 3(cotgx - cosx) - 5(tgx - sinx) =
72/ (√1−cosx+√cosx)cos 2x=1
2sin 4x 73/ tgx + 2cotg2x = sin2x
74/.2cosxcos2x = + cos2x + cos3x 75/ 3sinx + 2cosx = + 3tgx 76/ sin3x.cos3x + cos3x.sin3x = sin34x
77/ (3x −π
4)=sin 2x.sin(x+ π 4) sinx+sin2x+sin 3x
cosx+cos2x+cos3x=√3
78/.T×m nghiƯm: sinxcos4x + 2sin22x = - 4 sin2
(π4− x 2) tm : ¿
|x −1|<3
x2+3>− x
¿{
¿
79/.(1 + tgx)(1 + sin2x) = + tgx 80/.2sin3x - sinx = 2cos3x - cosx + cos2x
(3)