HOC360.NET - TÀI LIỆU HỌC TẬP MIỄN PHÍ 1 1 25 25 541 41 41
[Pages:4] - T?I LIU HC TP MIN PH?
1
1
25
25 5 41
* cos2 =
1 tan2
2 cos =
4 41
41 41
1
5
3
5 41
V? 2 cos > 0. Suy ra: cos =
2
41
sin
4 5 41 4 41
* tan
sin = tan .cos = .
cos
5 41
41
1
B?i 3: a) T?nh cos , bit sin v? 0
3
3
2
b) T?nh sin(a ? b), bit sin a 4 vi 00 a 900 v? sin b 2 vi
5
3
900 b 1800
c)
T?nh
tan a
,
bit
cosa
=
5
v?
a
;
3
4
13
2
1
3
Gii: a) Ta c?: A = cos cos.cos sin .sin cos sin
3
3
32
2
2
* T?nh cos : cos2
= 1 ? sin2
=1?
1
3
=
2 cos
3
=
26
33
6
V? 0 cos > 0 n?n cos =
2
3
1
3
1 6 3 1 3 6
Vy: A = cos sin = . .
2
2
23 2 3 6
b) Ta c?: B = sin(a ? b) = sina.sinb ? cosa.cosb
2
* T?nh cosa: cos2a = 1 ? sin2a = 1 ?
4
=
9
3 cosa =
5 25
5
V? 00 a 900 cosa > 0 n?n cosa = 3 5
2
* T?nh cosb: cos2b = 1 ? sin2b = 1 ?
2
=
5
cosb =
3 9
55
93
V? 00 a 900 cosb < 0 n?n cosb = 5 3
4 2 3 5 83 5 Vy: B = sina.sinb ? cosa.cosb = . .
5 3 5 3 15
Group:
- T?I LIU HC TP MIN PH?
c)
Ta
c?:
C
=
tan a
4
tan a tan 4
1 tan a.tan
tan a 1 1 tan a
4
1
1
1
144
* T?nh tana: 1 + tan2a =
tan2a =
? 1 =
cos2 a
cos2 a
2 1 tana =
5
25
13
12
5
12
V?
a
3 ;
2
tana
>
0.
Suy
ra:
tana
=
12 5
.
Vy:
C
=
tan a 1 1 tan a
5 1
1 12
17
7
5
B?i 4: T?nh sin2a, cos2a v? tan2a, bit:
3 a) sina = ? 0,6 v? a
2
Gii: a) Ta c?: sin2a = 2sina.cosa
1 3 b) sina + cosa = v? a
2 4
*
T?nh
cosa:
cos2a
=
1
?
sin2a
=
1
?
2
0, 6
=
16
cosa
=
4
25
5
3
4
4 24
V? a cosa < 0 n?n cosa = . Vy: sin2a = 2.( ? 0,6). =
2
5
5 25
2
*
cos2a
=
cos2a
?
sin2a
=
4
(0,6)2
7
5
25
24
* tan2a =
sin 2a
25
24
cos2a 7 7
25
1
1
1
b) Ta c?: sina + cosa = ( sina + cosa)2 = sin2a + cos2a + 2sinacosa =
2
4
4
1
3
sin2a = 1
4
4
2
*
T?nh
cos2a:
T?nh
cos2a:
cos22a
=
1
?
sin22a
=
1
?
3
=
7
cos2a =
4 16
7
7
16 4
3
3
7
V? a 2a 2 cos2a > 0 cos2a =
4
2
4
120
* tan2a =
119
3 B?i 5: T?nh gi? tr ca biu thc: a) A = sin cos
88
13 5 b) B = sin sin
24 24
Group:
- T?I LIU HC TP MIN PH?
3 1 3 3
Gii: a) Ta c?: A = sin cos 8
8
2
sin
8
8
sin 8
8
=
1 2
sin
4
sin
2
1 2
2 2
2 1
4
2
13 5 1 13 5 13 5
b) B = sin
24
sin 24 2 cos
24
cos 24
24
24
1 3 1 1 2 1 2
=
2 cos 3
cos
4
22
2
4
B?i 6: Bin i th?nh t?ch c?c biu thc sau:
a) A = 1 ? sinx
b) B = 1 ? 2sinx
c) C = sin3x + sin2x
d) D = 1 + cosx + cos2x + cos3x
e) E = cos2x + cos22x + cos23x ? 1
f) F = sin11x.sin5x + sin23x ? cos2x
Gii:
a)
A
=
1
?
sinx
=
sin
?
sinx
=
2cos
2
x
sin
2
x
=
2cos
x
sin
2
2 2
4 2
x
4 2
b)
1
?
2sinx
=
2
1
sin
x
=
2
sin
sin
x
2
6
=
4cos
6
x
sin
6
x
= 2cos
x sin
x
2 2
12 2 12 2
3x 2x 3x 2x
5x x
c) C = sin3x + sin2x = 2sin
cos
2sin cos
2 2
22
x
5x x
d) D = 1 + cosx + cos2x + cos3x = (1 + cosx) + (cos3x + cos2x) = 2cos2 + 2cos cos
2
22
x 5x
x
x 3x
= 2cos (cos + cosx ) = 4cos cos cosx
22
2
22
1
1
1
e) E = cos2x + cos22x + cos23x ? 1 = (1 cos2x) (1 cos4x) (1 cos6x) 1
2
2
2
11
11
11
11
1
1
= + cos2x + + cos4x + + cos6x ? 1 = + cos2x + cos4x + cos6x
22
2 2
22
22
2
2
1
1
= [(1 + cos2x) + (cos6x + cos4x)] = (2cos2x + 2cos5xcosx) = cosx(cos5x + cosx)
2
2
= 2cosxcos3xcos2x
1
1
1
f) F = sin11x.sin5x + sin23x ? cos2x = (cos6x ? cos16x) + (1 ? cos6x) ? (1 + cos2x)
2
2
2
Group:
- T?I LIU HC TP MIN PH?
1
1
11
11
1
= cos6x ? cos16x + ? cos6x ? ? cos2x = ? (cos16x + cos2x)
2
2
2 2
2 2
2
= ? sin9x.sin7x
B?i 7: Bin i th?nh tng c?c biu thc sau:
a) A = 2sinxsin2xsin3x
b) B = 8cosxsin2xsin3x
c) C = sin(a + 300).cos(a ? 300)
d) D = sin x .sin x .cos2x
6 6
Gii: a) A = 2sinxsin2xsin3x = (2sin2xsinx).sin3x = (cosx ? cos3x).sin3x
1
1
= sin3xcosx ? sin3xcos3x = (sin4x + sin2x) ? (sin6x + sin0)
2
2
1
1
1
= sin4x + sin2x ? sin6x
2
2
2
b) B = 8cosxsin2xsin3x = (8sin3xsin2x)cosx = 4(cosx ? cos5x).cosx = 4cos2x ? 4cos5x.cosx
= 2(1 + cos2x) ? 2(cos4x + cos6x) = 2 + 2cos2x ? 2cos4x ? 2cos6x
1
1
3
c) C = sin(a + 300).cos(a ? 300) = (sin2a + sin600) = sin2a +
2
2
4
d)
D
=
sin
x
.sin x
.cos2x
=
1
(cos
? cos2x).cos2x
=
1
cos2x
?
1
cos22x
6 6
23
4
2
1
1
1
11
= cos2x ? (1 + cos4x) = cos2x ? + cos4x
4
4
4
4 4
B?i 8: R?t gn c?c biu thc sau:
sin3x cos5x sin3x cos5x a) A
cos x
sin x sin 4x sin 7x b) B
cos x cos4x cos7x
2sin2 sin 4 c) C
2sin2 sin 4
sin5 sin3 d) D
2 cos 4
1 cos2
e) E tan
sin
sin
1 cosa sin a f) F
1 cosa sin a
sin3x cos5x sin3x cos5x sin(3x 5x) sin(2x) sin 2x
Gii: a) A
cos x
cos x
cosx cosx
2sin x cosx
2sin x
cos x
b)
sin x sin 4x sin 7x (sin 7x sin x) sin 4x 2sin 4x cos3x sin 4x
B
cosx cos4x cos7x (cos7x cosx) cos4x 2 cos4x cos3x cos4x
sin 4x(2cos3x 1) sin 4x
=
tan 4x
cos4x(2cos3x 1) cos4x
2sin2 sin 4 2sin2 2sin 2.cos2 2sin2(1 cos2)
c) C
2sin 2 sin 4 2sin2 2sin 2.cos2 2sin2(1 cos2)
Group:
................
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