81 bai tap PTLG du dang.

Ph¬ng tr×nh lîng gi¸c-PDT
1/. T×m x∈ (0; 2π) cña pt :
32
221
33
5
+=






+
+
+
xcos
xsin
xsinxcos
xsin
2/. sin
2
3x - cos
2
4x = sin
2
5x - cos
2
6x
3/. T×m x ∈ [0;14] : cos3x - 4cos2x + 3cosx - 4 = 0 .
4/. cosx+ cos2x + cos3x + cos4x + cos5x = -1/2

5/.(cos2x - 1)(sin2x + cosx + sinx) = sin
2
2x 6/.5sinx - 2 = 3(1 - sinx)tg
2
x
7/.cotgx - 1 =
tgx
xcos
+
1
2
+ sin
2
x -
2
1
sin2x 8/.cotgx - tgx + 4sin2x =
xsin 2
2
9/.
0
242
222
=−







π
−
x
cosxtg
x
sin
10/.
4 4
3
cos sin cos sin 3 0
4 4 2
x x x x
π π
   
+ + − − − =
 ÷  ÷
   
10/.
( )( )
xsinxsinxcosxsinxcos
−=+−
2212
12/. cos
2
3xcos2x - cos
2
x = 0
13/. 1 + sinx + cosx + sin2x + cos2x = 0 14/. cos3x + cos2x - cosx - 1 = 0
15/.
( )

6 6
2 sin sin .cos
0
2 2sin
cos x x x x
x
+ −
=
−
16/.cotx + sinx(1+tanx.tanx/2) = 4
17/.
( ) ( )
2 2
1 sin cos 1 cos sin 1 sin 2x x x x x+ + + = +
18/. 2sin
2
2x + sin7x - 1 = sinx
19/.
2
sin cos 3 cos 2
2 2
x x
x
 
+ + =
 ÷
 
20/.T×m m:
( )
02sin24coscossin4

44
=−+++
mxxxx
cã
Ýt nhÊt mét nghiÖm thuéc ®o¹n






2
;0
π


21/.
x
xg
x
xx
2sin8
1
2cot
2
1
2sin5
cossin
44
−=

+
22/.
( )
x
xx
xtg
4
2
4
cos
3sin2sin2
1
−
=+
23/. tgx + cosx - cos
2
x = sinx(1 + tgxtgx/2)
24/.
x
x
sin
cos8
1
2
=
25/.
xsin
xcos
tgxgxcot
2

42
+=
26/.
( )
0623 =++− xcosxsintgxtgx
27/. cos2x + cosx(2tg
2
x - 1) = 2 29/. sin(πcosx) = 1
30/.
032943
26
=++−
xcosxcosxcos
31/.
xsinxcostgxxtg 3
3
1
2
=−
32/.
5
5
3
3 xsinxsin
=
33/.
( ) ( )
02122
3
=−+++−+

xcosxsinxsinxcosxsin
34/.
01
=++
xcosxsin
35/.
( )
442
=−+
xsinxcosxsin
36/.Cho PT:
a
xx
xx
=
+−
++
3cos2sin
1cossin2
(2) (a lµ tham sè)
a) Gi¶i a =1/3. b) T×m a ®Ó ph¬ng tr×nh (2) cã nghiÖm ?
37/.Cho ph¬ng tr×nh:
( )
01122
=−+−+
mxcosmxcos
1) Gi¶i m = 1. 2) m=? ®Ó PT cã nghiÖm/







π
π
;
2
.
38/.
( )
1
1cos2
42
sin2cos32
2
=
−






−−−
x
x
x
π
39/.
( )

( )
xsin
xcosxsin
xcosxcos
+=
+
−
12
1
2
40/.
xcos
xcosxcos
1
7822
=+−
41/.
022
3
=−+
xcosxcosxsin
42/.Cho ph¬ng tr×nh:
( ) ( )
m
tgxtgx
=−++
223223
1) Gi¶i m = 6. 2) m=? ®Ó PT cã ®óng 2 ng PB/







ππ
−
22
;
.
43/.
0
239624
22
=
−−+
xcos
xcosxsinxsin

43/.A/.
( )
1
2
2
1
−
−
=
+
gxcot
xsinxcos

xgcottgx
44/.
23sin2sinsin
222
=++
xxx
45/.
03sin2cos4cossin
=+
xxxx
46/.
0221
=++++
xcosxsinxcosxsin
47/.tg2x + cotgx =
8cos
2
x
48/.
xtg
xsinxcos
xcosxsin
2
8
13
22
66
=
−
+

49/.





π
−=
π
−
=+
22
1
22
y
y
x
x
ysinxsin
50/. sinx.cosx + cosx = -2sin
2
x - sinx + 1
51/. sin3x = cosx.cos2x.(tg
2
x + tg2x)
52/.
( )
( )
1
12

232
=
−
+++
xsin
xsinxsinxsinxcosxcos
53/.






=
33
4
2
x
cos
x
cos
54/.
( )
032332
=++−++
xcosxcosxcosxsinxsinxsin
55/.
( )
1221
2

−=−−
xsinxsinxcosxsin
56/.
xsinxsin 2
4
3
=






π
+
57/.
( )
1
2
2
1
−
−
=
+
gxcot
xsinxcos
xgcottgx
58/. GBL: 2m(cosx + sinx) = 2m
2

+ cosx - sinx + 3/2
59/.
1
20002000
=+
xcosxsin
60/.






+
π
=






−
π
2
3
102
1
210
3 x

sin
x
sin
61/.
x
x
xx
cos4
sin
2sin12sin1
=
++−
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 +
1
=+
xsinxcos

69/.cos7x -
273
−=
xsin
tm:
π<<π
7
6
5
2
x

70/.9sinx + 6cosx - 3sin2x + cos2x = 8 71/. 3(cotgx - cosx) - 5(tgx - sinx) = 2
72/.
( )

xsinxcosxcosxcos 4
2
1
21
=+−
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/






π
+=






π

−
4
2
4
3 xsin.xsinx
3
32
32
=
++
++
xcosxcosxcos
xsinxsinxsin
78/.T×m nghiÖm: sinxcos4x + 2sin
2
2x = 1 - 4






−
π
24
2
x
sin
tm :




−>+
<−
xx
x
3
31
2

79/.(1 + tgx)(1 + sin2x) = 1 + tgx 80/.2sin
3
x - sinx = 2cos
3
x - cosx + cos2x
81/.sinx + cosx + cos2x - 2sinx.cosx = 0