HOC360.NET - TÀI LIỆU HỌC TẬP MIỄN PHÍ 0 1 3 ) = 2 4
[Pages:5] - T?I LIU HC TP MIN PH?
c) C = sin(a + 300).cos(a ? 300) = 1 (sin2a + sin600) = 1 sin2a + 3
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
cosx 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 sina f) F
1 cosa sina
sin3x cos5x sin3x cos5x sin(3x 5x) sin(2x) sin2x
Gii: a) A
cos x
cos x
cosx cosx
2sin x cosx
2sin x
cos x
sin x sin 4x sin 7x (sin 7x sin x) sin 4x 2sin 4x cos3x sin 4x
b) B
cosx cos4x cos7x (cos7x cosx) cos4x 2 cos4x cos3x cos4x
sin 4x(2cos3x 1) sin 4x
=
tan 4x
cos4x(2 cos3x 1) cos4x
2sin2 sin 4 2sin2 2sin2.cos2 2sin2(1 cos2)
c) C
2sin2 sin 4 2sin2 2sin2.cos2 2sin 2(1 cos2)
= 1 cos2 2sin2 tan2 1 cos2 2 cos2
sin 5 sin3 2cos4sin
d) D
sin
2 cos 4
2 cos 4
1 cos2
sin 1 cos2
1 cos2 sin2
e) E tan
sin
sin
sin
cos sin
cos cos
Group:
- T?I LIU HC TP MIN PH?
1 cos2 sin2 1 cos2 sin2 2 cos2
=
2cos
cos cos
cos
cos
f)
F
1
cosa sin a
2 cos2
a 2
aa 2sin cos
22
aa 2cos (cos
22
a sin )
2
cot
a
1 cosa sin a
2sin2 a 2sin a cos a
aa a 2sin (sin cos )
2
2
22
22 2
B?i 9: Chng minh c?c ng nht thc:
4sin2 3a
1
a) cot a tan5a
sin6a sin 4a sin a.cos5a
1 cosx cos2x
b)
cot x
sin 2x sin x
sin3 a cos3 a
c)
1 sin acosa
sin a cosa
d) sin4x + cos4x ? sin6x ? cos6x = sin2x.cos2x
e) sinx(1 + 2cos2x + 2cos4x + 2cos6x) = sin7x
f) 1 sin2 .cos2 cos2 tan2 cos2
4sin2 3a cosa sin 5a 4sin2 3a
Gii: a) VT = cot a tan 5a
sin 6a sin 4a sin a cos5a sin 6a sin 4a
cos5a.cosa sin5a.sin a 2(1 cos6a) cos6a 1 cos6a
=
cos5a.sin a
2cos5a.sina cos5a.sina cos5a.sin a
cos6a 1 cos6a
1
=
= VT (pcm)
cos5a.sin a sina.cos5a
1 cosx cos2x 2 cos2 x cosx cosx(2 cosx 1) cosx
b) VT =
cot x = VP (pcm)
sin 2x sin x 2sin x cosx sin x sin x(2 cosx 1) sin x
sin3 a cos3 a (sin x cosx)(sin2 x sin x.cosx cos2 x)
c) VT =
1 sin x.cosx =VP(pcm)
sina cosa
sina cosa
d) VT = sin4x + cos4x ? sin6x ? cos6x = sin4x + cos4x ? (sin6x + cos6x)
= sin4x + cos4x ? [(sin2x)3 + (cos2x)3]
= sin4x + cos4x ? (sin2x + cos2x)(sin4x ? sin2x.cos2x + cos4x)
= sin4x + cos4x ? sin4x + sin2x.cos2x ? cos4x = sin2x.cos2x = VP (pcm)
e) VT = sinx(1 + 2cos2x + 2cos4x + 2cos6x)
= sinx + 2cos2x.sinx + 2cos4x.sinx + 2cos6x.sinx
= sinx + (sin3x ? sinx) + (sin5x ? sin3x) + (sin7x ? sin5x) = sin7x = VP (pcm)
Group:
- T?I LIU HC TP MIN PH?
f) VT = 1 sin2 .cos2 cos2 1 sin2 .cos2 cos4 1 cos2 (sin2 cos2 )
cos2
cos2
cos2
= 1 cos2 sin2 tan2 = VP (pcm) cos2 cos2
III: B?I TP T LUYN
B?i 1: T?nh c?c gi? tr lng gi?c ca cung , bit:
a) sin = 0,6 khi 0
2
7 b) cos = khi
10 2
3 c) tan = 2 khi
2
3 d) cot = -3 khi 2
2
B?i 2: T?nh c?c gi? tr lng gi?c ca cung a, bit:
1
3
a) cosa , a
4
2
2 b) sin a , a
32
7
c) tan a , 0 a
3
2
14 3 d) cot a , a 2
92
12 3 a
B?i 3: a) Cho sina = v? . T?nh cos a
13 4 2
3
8
8
3
b) Cho sin = , 0 v? sin = , . T?nh sin( + )
17
2
17
2
c)
Cho
cos
=
1 ,
;
.
T?nh
tan
3 2
4
3
B?i 4: a) Cho cosa = v? a . T?nh sin a
5 2
6
b) T?nh cos(a + b), bit
sina
4
vi
00
a 900
v?
2 sin b
vi
900 b 1800
5
3
c)
Cho
cosx
=
4
v?
3
x
2 .
T?nh
tan x
5 2
4
Group:
- T?I LIU HC TP MIN PH?
3
B?i 5: a) Cho cos = v? 0 . T?nh cos2 , sin 2 v? tan2
4
2
3
3
b) Cho sin = v? . T?nh cos2 , sin 2 v? tan2
5
2
1 B?i 6: a) Cho sina ? cosa = v? a . T?nh sin2a, cos2a, tan2a
54 2
2
b) Cho sinb + cosb = v? 0 b . T?nh sin2b, cos2b, tan2b
7
4
B?i 7: T?nh gi? tr ca c?c biu thc: a) A = cos750.cos150
11 5 b) B = sin .cos
12 12
1
3
c) C =
s in100 cos100
d) D = 96 3 sin .cos .cos .cos .cos
48 48 24 12 6
B?i 8: Bin i th?nh t?ch c?c biu thc sau:
a) A = 1 + sinx
b) B = 1 + 2cosx
c) C = cos5x ? cos2x
d) D = 1 + cos2x + cos4x + cos6x
e) E = 1 + sinx ? cos2x
f) F = 1 ? 2cosx + cos2x
g) M = sinx.cos3x + sin4x.cos2x
h) N = sin2x ? sin22x + sin23x
i) P = cosa + cosb + sin(a + b)
B?i 9: Bin i th?nh tng c?c biu thc sau:
a) A = 2cos2x.cos3x.sin4x
b) B = 8cos3x.sin5x.sin7x
c) C = 4sin(x + 300).cos(x ? 300).cos2x
d) D = 4cos(a ? b).cos(b ? c).cos(c ? a)
B?i 10: R?t gn c?c biu thc sau:
cos2x cos4x sin2xsin 4x a) A
sin 4x
sin x sin3x sin 5x b) B
cosx cos3x cos5x
1 sin2 cos2 c) C
1 sin2 cos2
sin8 sin 2 d) D
2 sin 5
1 sin2
e) E cot
cos
cos
sin 2a sina f) F
1 cos2a cosa
B?i 11: Chng minh c?c ng nht thc:
Group:
- T?I LIU HC TP MIN PH?
a) cos4a.tan 2a sin 4a tan2 2a cos4a.cot 2a sin 4a
1 cosx cos2x cos3x
b)
2cosx
2cos2 x cosx 1
sin3 a cos3 a
c)
1 sin acosa
sin a cosa
d)
cos2
x.sin x
sin3
x. cos x
1 sin 4x
4
e) cosx(2cos2x + 2cos4x + 2cos6x ? 1) = ? cos7x
f) 1 cosx .tan2 x cos2 x sin2 x 1 cosx 2
g)
cos x
1 cos3x
1 cos 5x
8sin2
x.cos3 x
2
2
h) 3 ? 4cos2a + cos4a = 8sin4a
i) cos2x sin 4x cos6x tan(x 150 ).cot(x 150 ) cos2x sin 4x cos6x
a
7a
j) cos2a ? cos3a ? cos4a + cos5a = 4sin .sina.cos
2
2
II
A' -
180 0
III
y
2 900
B
I tru?c sin +
+ A0 x O tru?c co?sin 2
360 0
-
IV B'
3 270 0 2
Group:
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