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# (新人教版)【文库精品】年高中数学 第3章 三角恒等变换单元评估验收 新人教A版必修4【必做资料】

3

()

(120 150 )

( 12 5 60

)

12sin2151 ( )

A.12

B12

3 C. 2

3 D 2

2sin2151(12sin215)cos

30

3 2.

D

2ABC sin Asin Bcos Acos BABC ( )

A

B

C

D

sin Asin Bcos Acos B sin Asin Bcos Acos B0cos(AB)0

cos C0 C ABC

B

3 cos52 352 0 sin 2 (

)

A.2245

B.1225

12 C25

24 D25

sin 352 0

cos 45

sin 2 2sin cos 235452254.
D

4 f(x)sin xcos x 23cos 2x (

)

1

A 1 B 2 C2 1 D2 2

f(x)sin xcos x 23cos 2x

12sin 2x 23cos 2x

sin2x3 f(x) 1 A.
A

5ABC C120tan

Atan

B2

3

3

tan

Atan

B (

)

A.14 B.13 C.12 D.53 ABC C120 AB60 (tan Atan B)tan(AB)(1tan Atan B)

3(1tan Atan B)2 3 3.

tan Atan B13.

B

6 cos 55 tan4 2 (

)

A3

B17

C43

D7

cos 55 sin 2 5 5 tan 2tan 2 12tatnan2

4

14 443 tan4 2

11ttaann

2 2

1134317 B.

B

7 cos 4 13 02 sin (

)

A.46 2

B.46 2

C.178

D.

2 3

2

4 4 34

sin 4

1cos2 4 2 3 2

sin sin 4 4

sin

4 cos

4

cos

4 sin

4

2 3 2

2213

2 2

46 2.

A

5

1

8 sin cos 2 tan tan ( )

A5

B6

C7

D8

sin cos 25 1sin 2 54 sin 2

1 4

tan

tan1

ttaann21scionssin
cos

21sin22

2148.

D

9 cosx6 35x(0 ) sin x (

)

4 33 A. 10

4 33 B. 10

1

3

C.2

D. 2

cosx6 35 0<x< 0<x6 <2 sinx6 45

sin

xsinx6 6 sinx6 cos

6

cosx6

sin

6

45

2335

3

124 1303.

B

10 sin5 14 cos2 35 (

)

A78 B.78 C.18 D18

cos2 35 cos2 310 cos 22 5 2cos22 5 1 2sin25 1
7 8.

A

11 ysinx12sinx512 (

)

A.12

B.14

C1

2 D. 2

ysinx12sinx512

sinx12sinx122

sinx12cosx12

12sin2x6

sin2x6

1

1 2

A.

A

12 f(x)sin( x )cos( x ) 0| |2 f(x)f(x)( )

4

Af(x)02 Bf(x)4 34

Cf(x)02 Df(x)4 34 f(x)sin( x )cos( x )

2cos

x

cos

4

sin

x

sin

4

2cos x 4

2cos x 4

f(x)

2

2.

f(x)f(x) f(x)

4 k (kZ)

| |2 4

f(x) 2cos 2x

02x 0x2 f(x) A.

A

( 4 5 20 ) 13 2cos2xsin 2xAsin( x )b(A0) A________b________

2cos2xsin 2x1cos 2xsin 2x 2sin2x4 1Asin( x )

b A 2b1.

2 1

14 tan 4 16 tan ________

tan 4 t1antan116 tan 75.

5

75

15 f(x)sin2x4 2 2sin2x ________

f(x)sin2x4 2 2sin2x

2 2 sin

2x

2 2 cos

2x2

1cos 2x 2 2

2 2 sin

2x

2 2 cos

2x

2

sin2x4 2
. 16. () 1 25 cos 2 ________

1 25

a2b225

6. ab12ab6

4

7

34. cos 5cos 2 2cos2 125.

275

( 6 70 )

17( 10 ) 0 2 sin 45.

(1)scions22

sin cos

2 2

(2) tan 54

(1) 0 2 sin 45 cos 35.

6

scions22

sin cos

2 2

sin2

2sin 3cos2

cos 1

45323522451 3520.

(2) tan

csoisn

43

tan 54 t1antan143114317.

18( 12 ) f(x) 2cosx12xR.

(1) f6

(2)

cos

3 5

32

2

f2

3

.

(1)f6

2cos6 12

2cos4

2cos

4

1.

(2)f2 3

2cos2 3 12

2cos2 4

cos 2 sin 2 .

cos 35 32 2

4 sin 5.

sin 2 2sin cos 2245.

cos 2 cos2 sin2 275.

f2 3 cos 2 sin 2 27522452157.

19( 12 ) f(x) 3sin 2x2cos2x.

(1) f(x)

7

(2) tan 2 3 f( ) (1)f(x) 3sin 2x2cos2x

3sin 2xcos 2x1

2sin2x6 1.

2x6 2k 2

xk 3 kZ

f(x) 1.

(2)f( ) 3sin 2 2cos2

2

3sin cos 2cos2 sin2 cos2

2

3tan tan2

12

tan 2 3

f( )2 34 233121103.

20( 12 ) m(sin Acos A)n( 31) mn1 A
(1) A (2) f(x)cos 2x4cos Asin x(xR)

(1) mn 3sin Acos A2sinA6 1 sinA6 12.

A A6 6 A3 .

(2)(1) cos A12 f(x)cos 2x2sin x12sin2x2sin x 2sin x12232. xR sin x[11] sin x12f(x)32 sin x1 f(x)3

8

f(x)332. 21( 12 ) a(sin xcos x)b(cos xcos x)xR f(x)a(ab) (1) f(x) (2) f(x)32 x

(1) f(x)a(ab)aaabsin2xcos2xsin xcos xcos2x112

sin 2x12(cos 2x1)32 22sin2x4

f(x)32

2 2

T22

.

(2)(1) f(x)3232 22sin2x4 32sin2x4 02k 2x4 2k k 8 xk 38 (kZ)

f(x)32 x

xk

8

xk

38

kZ.

22 ( 12 ) f(x)2cos x(sin xcos x)

(1) f54

(2) f(x)

(1)f54

2cos

5 4

sin

5 4

cos

5 4

2cos

4

sin

4

cos

4

2.

(2) f(x)2sin xcosx2cos2xsin 2xcos 2x1 2sin2x4 1 T22 f(x) .

2k 2 2x4 2k 2 kZ

k 38 xk 8 kZ.

f(x)k 38 k 8 kZ.

9

f(x)2sin xcos x2cos2x

sin 2xcos 2x1 2sin2x4 1.

(1)f54

2sin

11 4

1

2sin

4

12.

(2) T22 f(x) .

2k 2 2x4 2k 2 kZ

k 38 xk 8 kZ.

f(x)k 38 k 8 kZ.

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