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Mình con nhiều có thể trao đổi sau qua emaila/kiÕn thøc cÇn nhí vµ ph©n lo¹i bµi to¸n d¹ng 1 Ph ¬ng tr×nh bËc nhÊt vµ bËc hai , bËc cao víi 1 hµm sè l îng gi¸c

§Æt HSLG theo t víi sinx , cosx cã ®iÒu kiÖn 1 Gi¶i ph¬ng tr×nh ……….theo tNhËn t tho¶ m·n ®iÒu kiÖn gi¶i Pt lîng gi¸c c¬ b¶n Gi¶i ph¬ng tr×nh:

1/ 2/ 4sin3x+3 sin2x=8sinx

3/ 4cosx.cos2x +1=0 4/

5/ Cho 3sin3x-3cos2x+4sinx-cos2x+2=0 (1) vµ cos2x+3cosx(sin2x-8sinx)=0 (2).

T×m n0 cña (1) ®ång thêi lµ n0 cña (2) ( nghiÖm chung sinx= )

6/ sin3x+2cos2x-2=0 7/ a/ tanx+ -2 = 0 b / +tanx=7

c* / sin6x+cos4x=cos2x

8/sin( )-3cos( )=1+2sinx 9/

10/ cos2x+5sinx+2=0 11/ tanx+cotx=4 12/

13/ 14/ cos2x+3cosx+2=0

15/ 16/ 2cosx- =1

d¹ng 2: Ph¬ng tr×nh bËc nhÊt ®èi víi sinx vµ cosx : asinx+bcosx=cC¸ch 1: asinx+bcosx=c

§Æt cosx= ; sinx= C¸ch : 2

§Æt

C¸ch 3: §Æt ta cã

§¨c biÖt :

1.

2.

3.

§iÒu kiÖn Pt cã nghiÖm : gi¶i ph ¬ng tr×nh : 1/ 2sin15x+ cos5x+sin5x=k víi k=0 vµ k=4 víi k=0

2/ a : b:

c:

Chuyªn ®Ò ph ¬ng trinh l îng gi¸c 1

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3/ *t×m nghiÖm

4/( cos2x- sin2x)- sinx-cosx+4=0 5/

6/

D¹ng 3 Ph¬ng tr×nh ®¼ng cÊp ®èi víi sin x vµ cosx

Gi¶i ph ¬ng tr×nh 1/a/ 3sin2x- sinxcosx+2cos2x cosx=2 b/ 4 sin2x+3 sinxcosx-2cos2x=4 c/3 sin2x+5 cos2x-2cos2x-4sin2x=0 d/ 2 sin2x+6sinxcosx+2(1+

)cos2x-5- =02/ sinx- 4sin3x+cosx=0 2 c¸ch +/ (tanx -1)(3tan2x+2tanx+1)=0

+ sin3x- sinx+ cosx- sinx=0 (cosx- sinx)

(2sinxcosx+2sin2x+1)=03/ tanx sin2x-2sin2x=3(cos2x+sinxcosx) 4/ 3cos4x-4sin2xcos2x+sin4x=0 5/ 4cos3x+2sin3x-3sinx=0 6/ 2 cos3x= sin3x 7/ cos3x- sin3x= cosx+ sinx 8/ sinx sin2x+ sin3x=6 cos3x 9/sin3(x- /4)= sinx Dang 4 Ph ¬ng tr×nh vÕ tr¸i ®èi xøng ®èi víi sinx vµ cosx

* a(sin x+cosx)+bsinxcosx=c ®Æt t= sin x+cosx

at + b =c bt2+2at-2c-b=0

* a(sin x- cosx)+bsinxcosx=c ®Æt t= sin x- cosx

at + b =c bt2 -2at+2c-b=0

Gi¶i ph ¬ng tr×nh

1/ a/1+tanx=2sinx + b/ sin x+cosx= -

2/ sin3x+cos3x=2sinxcosx+sin x+cosx 3/ 1- sin3x+cos3x= sin2x 4/ 2sinx+cotx=2 sin2x+1 5/ sin2x(sin x+cosx)=2 6/ (1+sin x)(1+cosx)=2 7/ (sin x+cosx)=tanx+cotx

8/1+sin3 2x+cos32 x= sin 4x 9/* a* 3(cotx-cosx)-5(tanx-sin x)=2

9/b*: cos4x+sin4x-2(1-sin2xcos2x) sinxcosx-(sinx+cosx)=0

10/ 11/ cosx+ +sinx+ =

12/ sinxcosx+ =1

dang 5 Gi¶i ph¬ng tr×nh b»ng ph¬ng ph¸p h¹ bËc Chuyªn ®Ò ph ¬ng trinh l îng gi¸c

§¼ng cÊp bËc 2: asin2x+bsinx.cosx+c cos2x=0 C¸ch 1: Thö víi cosx=0 Víi cosx 0 .Chia 2 vÕ cho cos2x ta ®îc: atan2x+btanx +c=d(tan2x+1) C¸ch2: ¸p dông c«ng thøc h¹ bËc §¼ng cÊp bËc 3: asin3x+b.cos3x+c(sinx+ cosx)=0 hoÆc

asin3x+b.cos3x+csin2xcosx+dsinxcos2x=0 XÐt cos3x=0 vµ cosx 0 Chia 2 vÕ cho cos2x ta ®îc Pt bËc 3 ®èi víi tanx

2

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C«ng thøc h¹ bËc 2

cos2x= ; sin2x=

C«ng thøc h¹ bËc 3

cos3x= ; sin3x=

Gi¶i ph ¬ng tr×nh 1/ sin2 x+sin23x=cos22x+cos24x 2/ cos2x+cos22x+cos23x+cos24x=3/23/sin2x+ sin23x-3 cos22x=0

4/ cos3x+ sin7x=2sin2( )-2cos2

5/ sin24 x+ sin23x= cos22x+ cos2x víi

6/sin24x-cos26x=sin( ) víi 7/ cos4x-5sin4x=1

8/4sin3x-1=3- cos3x 9/ sin22x+ sin24x= sin26x

10/ sin2x= cos22x+ cos23x 11/ (sin22x+cos42x-1): =0

12/ 4sin3xcos3x+4cos3x sin3x+3 cos4x=3 13/ 2cos22x+ cos2x=4 sin22xcos2x

14/ cos4xsinx- sin22x=4sin2( )-7/2 víi <3

15/ 2 cos32x-4cos3xcos3x+cos6x-4sin3xsin3x=0

16/ sin3xcos3x +cos3xsin3x=sin34x 17/ * 8cos3(x+ )=cos3x

18/cos10x+2cos24x+6cos3xcosx=cosx+8cosxcos23x

19/ =1

20 / cos7x+ sin22x= cos22x- cosx 21/ sin2x+ sin22x+ sin23x=3/222/ 3cos4x-2 cos23x=1

Dang 6 : Ph ¬ng tr×nh LG gi¶i b»ng c¸c h»ng ®¼ng thøc

* a3 b3=(a b)(a2 ab+b2) * a8+ b8=( a4+ b4)2-2 a4b4

* a4- b4=( a2+ b2) ( a2- b2) * a6 b6=( a2 b2)( a4 a 2b2+b4) Gi¶i ph ¬ng tr×nh

1/ sin4 +cos4 =1-2sinx 2/ cos3x-sin3x=cos2x-sin2x

3/ cos3x+ sin3x= cos2x 4/ v« nghiÖm

5/cos6x-sin6x= cos22x 6/sin4x+cos4x=

7/ cos6x+sin6x=2(cos8x+sin8x) 8/cos3x+sin3x=cosx-sinx 9/ cos6x+sin6x=cos4x 10/ sinx+sin2x+sin3x+sin4x= cosx+cos2x+cos3x+cos4x

11/ cos8x+sin8x= 12/ (sinx+3)sin4 -(sinx+3) sin2 +1=0

Dang 7 : Ph ¬ng tr×nh LG biÕn ®æi vÒ tÝch b»ng 0 1/ cos2x- cos8x+ cos4x=1 2/sinx+2cosx+cos2x-2sinxcosx=03/sin2x-cos2x=3sinx+cosx-2 4/sin3 x+2cosx-2+sin2 x=0

5/ 3sinx+2cosx=2+3tanx 6/ sin2x+ cos2x+ cosx=0

Chuyªn ®Ò ph ¬ng trinh l îng gi¸c 3

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7/ 2sin2x-cos2x=7sinx+2cosx-4 8/

9/ 2cos2x-8cosx+7= 10/ cos8x+sin8x=2(cos10x+sin10x)+ cos2x

11/ 1+ sinx+ cos3x= cosx+ sin2x+ cos2x 12/ 1+sinx+cosx+sin2x+cos2x=0 13/ sin2 x(tanx+1)=3sinx(cosx-sinx)+3

14/ 2sin3x- =2cos3x+ 15/cos3x+cos2x+2sinx-2=0

16/cos2x-2cos3x+sinx=0 17/ tanx–sin2x-cos2x+2(2cosx- )=0

18/sin2x=1+ cosx+cos2x 19/1+cot2x=

20/ 2tanx+cot2x=2sin2x+ 21/cosx(cos4x+2)+ cos2x-

cos3x=0 22/ 1+tanx=sinx+cosx 23/ (1-tanx)(1+sin2x)=1+tanx

24/ 2 = 25/ 2tanx+cotx=

26/ cotx-tanx=cosx+sinx 27/ 9sinx+6cosx-3sin2x+cos2x=8 Dang 8 : Ph ¬ng tr×nh LG ph¶i thùc hiÖn c«ng thóc nh©n ®«i, h¹ bËc

cos2x= cos2x- sin2x =2cos2x-1=1-2sin2x sin2x=2sinxcosx

tan2x=

sinx = ; cosx= tanx=

Gi¶i ph ¬ng tr×nh

1/ sin3xcosx= + cos3xsinx 2/ cosxcos2xcos4xcos8x=1/16

3/tanx+2cot2x=sin2x 4/sin2x(cotx+tan2x)=4cos2x 5/ sin4x=tanx 6/ sin2x+2tanx=3 7/ sin2x+cos2x+tanx=2 8/tanx+2cot2x=sin2x 9/ cotx=tanx+2cot2x

10/a* tan2x+sin2x= cotx b* (1+sinx)2= cosx

Dang 9 : Ph ¬ng tr×nh LG ph¶i thùc hiÖn phÐp biÕn ®æi tæng_tÝch vµ tÝch_tæng Gi¶i ph ¬ng tr×nh 1/ sin8x+ cos4x=1+2sin2xcos6x 2/cosx+cos2x+cos3x+cos4x=0

3/ t×m 4/ sinx+sin2x+sin3x+sin4x=0

5/ sin5x+ sinx+2sin2x=1 6/

7/ tanx+ tan2x= tan3x 8/ 3cosx+cos2x- cos3x+1=2sinxsin2x Dang 10 : Ph ¬ng tr×nh LG ph¶i ®Æt Èn phô gãc A hoÆc ®Æt hµm B Gi¶i ph ¬ng tr×nh

1/ sin( )= sin( ) 2/ sin( )=sin2x sin( )

3/(cos4x/3 – cos2x): =0 4/ cosx-2sin( )=3

5/ cos( )=sin(4x+3 ) 6/3cot2x+2 sin2x=(2+3 )cosx

Chuyªn ®Ò ph ¬ng trinh l îng gi¸c 4

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7/2cot2x+ +5tanx+5cotx+4=0 8/ cos2x+ =cosx+

9/sinx- cos2x+ +2 =5 11/ +2 =3

Dang 11 : Ph ¬ng tr×nh LG ph¶i thùc hiÖn c¸c phÐp biÕn ®æi phøc t¹p Gi¶i ph ¬ng tr×nh

1/ 2/cos =1 t×m n0 x Z

3/ +2sinx=0 4/3cotx- tanx(3-8cos2x)=0

5/ 6/sin3x+cos3x+ sin3xcotx+cos3xtanx=

7/tan2xtan23 xtan24x= tan2x-tan23 x+tan4x 8/tanx+tan2x=-sin3xcos2x

9/sin3x=cosxcos2x(tan2x+tan2x) 10/

11/cos2 -1=tan2

12/

Dang 12 : Ph ¬ng tr×nh LG kh«ng mÉu mùc, ®¸nh gi¸ 2 vÕ ,tæng 2 l îng kh«ng ©m,vÏ 2 ®å thÞ b»ng ®¹o hµm Gi¶i ph ¬ng tr×nh

1/ cos3x+ =2(1+sin22x) 2/ 2cosx+ sin10x=3

+2sinxcos28x

3/ cos24x+cos26x=sin212x+sin216x+2 víi x 4/ 8cos4xcos22x+ +1=0

5/ 6/ 5-4sin2x-8cos2x/2 =3k t×m k Z* ®Ó hÖ cã nghiÖm

7/ 1- =cosx 8/( cos2x-cos4x)2=6+2sin3x

9/

Chuyªn ®Ò ph ¬ng trinh l îng gi¸c 5