1. BAØI TAÄP LÖÔÏNG GIAÙC
Π 1
1) 2sin2x-5sinxcosx-cos2x=-2 ⇔x= + kΠ; x = arctan + kΠ
4 4
Π −3
2) 2sin2x+sinxcosx-3cos2x=0 ⇔ x = + kΠ; x = arctan + kΠ
4 2
Π
3) 3sin2x-4sinxcosx+5cos2x=2 ⇔ x = + kΠ; x = arctan 3 + kΠ
4
Π
4) sin2x+sin2x-2cos2x=1/2 ⇔ x = + kΠ; x = arctan(−5) + kΠ
4
Π Π
5) 4sin2x+3 3 sin2x-2cos2x=4 ⇔ x = + kΠ; x = + kΠ
2 6
Π 8
6) 25sin2x+15sin2x+9cos2x=25 ⇔ x = + kΠ; x = arctan + kΠ
2 15
3
7) 4sin2x-5sinxcosx-6cos2x=0 ⇔ x = arctan 2 + kΠ; x = arctan(− ) + kΠ
4
Π Π
8) sin2x- 3 sinxcosx+2cos2x=1 ⇔ x = + kΠ; x = + kΠ
2 6
9) 2sin2x+3 3 sinxcosx-cos2x=4 VN
Π  8
10) 3sin2x+4sin2x+ (8 3 −9 ) cos2x=0 ⇔x=−
3
+ kΠ; x = arctan 3 −  + kΠ
 3
Π −1
11/ 4sin2x+2sin2x+2cos2x=1 ⇔ x = − + kΠ; x = arctan + kΠ
4 3
12/ 4sin2x+3 3 sin2x-2cos2x=4
Π −1
13/ 4cos2x+3sinxcosx-sin2x=3 ⇔x= + kΠ; x = arctan + kΠ
4 4
Π
14/ 2sin2x-sinxcosx-cos2x=2 ⇔x= + kΠ; x = arctan(−3) + kΠ
2
15/ 4sin2x-2sin2x+3cos2x=1 VN
Π 1
16/ 5sin2x+2sinxcosx+cos2x=2 ⇔x =− + kΠ; x = arctan + kΠ
4 3
Π 1
17/ sin2x-2sin2x+3cos2x=1 ⇔ x = + kΠ; x = arctan + kΠ
2 2
18/ 3sin2x-3sinxcosx+4cos2x=1 VN
Π Π
20/sin2x-2sin2x=2cos2x ⇔x= + kΠ; x = + kΠ
2 4
Π Π 1 Π
21/2sin2 2x-3sin2xcos2x+cos22x=2 ⇔x = + k ; x = arc cot(−3) + k 22)
4 2 2 2
2 sin( x +10 0 ) − 12 cos( x +10 0 ) = 3
Π Π Π
23) sin 5 x + 3 cos 5 x = 2 cos 3 x ⇔x= + kΠ; x = +k
12 48 4
Π 2Π
24) 3 sin 3 x − cos 3 x =1 ⇔ x =− +k
3 3
 3
 sin α =
 13
α Π +α Π
25) 13 sin 4 x + 3 cos 2 x = 4 sin x cos x ⇔ x = −
2
+ kΠ; x =
6
+k
3
víi: 
 cos α = 2

 13

2.  3
 sinα = 5 Π
26) 3 sin x + 4 cos x = 5 ⇔ x = α + k 2Π víi:  /0 < α <
 cosα = 4 2
 5
5Π Π Π Π
27) sin 4 x + 3 cos 4 x = 2 ⇔x= +k ; x =− +k
48 2 48 2
Π
28) 3 cos x +2 sin x =2 ⇔ x = + kΠ
2
Π 5
29) 3 cos x +2 sin x =3 ⇔ x = + kΠ; x = k 2Π; x = ± arccos + k 2Π
2 13
Π Π
30) 2cos3x+cos2x+sinx=0 ⇔ x = + k 2Π; x = + kΠ
2 4
 Π  Π Π
30) tan 2 x − 3  cot  x +
  
 =1
3
⇔ x = kΠ; x = + kΠ
3
31) cos7xcos6x=cos5xcos8x
x x
sin 1 − sin
2 2 Π
32) = ⇔x= + kΠ
x x 2
1 + sin cos
2 2
x
2 tan
2 x Π 4Π
33) = cos ⇔x= +k
x 2 3 3
1 + tan 2
2
Π
34) cos6xcos2x=1 ⇔x =k
2
35) sin6xsin2x=1 VN
Π Π Π
36) 2(sin22x+sin2x)=3 ⇔x=
+ k ; x =  + kΠ
4 2 3
Π Π
37) 6cos2x-cosx=-cos3x ⇔ x = + kΠ; x =  + k 2Π
2 3
Π
38) 2tanx+tan2x=tan4x ⇔x=k
3
3x 5x x 3x x 3x
39) 2 sin sin = sin sin − cos cos ⇔ x = Π + k 2Π
4 4 2 2 2 2
Π Π Π Π 2Π Π 2Π
40) 2 cos 5 x = sin( 2 x + Π) + sin( 2 x + ) cot 3 x ⇔ x = +k ;x = +k ;x = +k
2 10 5 12 3 4 3
Π Π Π Π 5Π 2Π
41) 2 cos(2 x + ) = cos( x + ) − sin( x + ) ⇔ x = + k 2Π; x = +k
4 4 4 4 12 3
Π −Π
42) (tan x + 3 ) − 3 = (1 + 3 ) tan x + 3
2
⇔ x = + kΠ; x =
4 13
+ kΠ
sin x Π
43) sin 2 x + =2 ⇔ x = + kΠ
cos x 4
Π
44) cos2xsin2x+1=0 ⇔ x = + kΠ
2

3. Π Π
45) tan2x-2sin2x=sin2x ⇔ x = kΠ; x = +k
8 2