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

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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

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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:

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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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