cong thuc luong giac

Tìm nghiệm của phương trình sau trong khoảng đã cho..[r]

PHƯƠNG RÌNH LƯỢNG GIÁC Bài Tìm giá trị lớn nhất, nhỏ hàm số.

y 2cos x 1

3          1

y 5 cos xsinx 2

 

y 3 cos 2x 2

4 

 

     

 

y 2cos3x  Bài Tìm TXĐ

1 cosx y

sin 2x 

 y 1 cos3x

1 cos3x 

  2

y cot 3x 3



 

    

  y tan x 6



 

   

 

Bài Giải phương trình  0

2sin x 30  sin 2x cos x

3

 

   

  

   

    tan 3x cot 5x 1  

 

  

 

 

 0

sin x 45 cos2x tan 2x 15  01 0 sin 2x cos x



 

   

 

sin 2x cos2x



 

 

 

  tan 2x cot 3x 0  tan 2x 3

         2x

2 sin

3  

 



 

  3cos 3x 3

         

3cot x          

tan 3x cot 2x

5

 

   

  

   

    tan 3x cos2x 1  

 

  

 

  cos 3x sin x

                     

6cos 4x 3           cos x          sin 3x cos x

4               

Bài : Giải phơng tr×nh sau

1 cos 2x3sinx2 ;2

4 sin x12 cos x7;

25 sin x100 cosx89

4 4

sin 2xcos 2xsin cos 2x x ;5.   

6

2

sin cos tan cos sin

x x

x

x x

6 tan2  9 cos

x

x ,7,2sin

2x – cos2x - 4sinx + = 0;8,9cos2x - 5sin2x - 5cosx + = 0

9) 5sinx(sinx - 1) - cos2x = 3;10)cos2(3x +



) – cos23x – 3cos(



- 3x) + = 11;cos2x + sin2x + 2cosx + = 0;12; 3cos2x + 2(1 + 2 + sinx)sinx – (3 + 2) = 0 13, tg2x + ( 3 - 1)tgx – 3 = 0;14) 3cot 3

sin

2x  gx

15; cos cos sin sin

4 2

    x x x x ;16; 1 sin ) (sin sin ) sin (cos cos      x x x x x x

Bài Giải phương trình (Dạng: at2 + bt + c = 0)

2

2sin x 3sinx 0   6cos x cosx 02    2cos 2x cos2x 02  

2

tan x cotx 2  cosx 3cosx 2 0

2

   cos2x cosx 0  

2

3sin 2x 7cos2x 0   Bài Giải phương trình

2 x

cos2x 3cosx 4cos 2

  6sin x 2sin 2x 52   6sin 3x cos12x 42  

 

2

2cos 2x 2 3 cos2x  3 0 5 cos x    2 sin x cos x4 

3

7cos x 4cos x 4sin 2x  4sin x sin2x 8sinx3  

2

4

t anx 7

cos x   cos2x sin x 2cos x 0   

2

sin 2x 4sinx cos x 2sin x 

I PT bậc Sin cos Bài Giải phương trỡnh (Phương trỡnh đẳng cấp sinx cosx)

2

2cos x 5sin x cos x 6sin x 0    cos x2  3 sin 2x sin x 0  

2

cos x sin x cos x 2sin x 0    cos x2  3 sin x cos x 0 

 

2 sinx cos x cos x 2cos x   4sin x 3sin 2x 2cos x 42   

2

3sin x 5cos x 2cos 2x 4sin 2x 0    3sin x2  3 sin x cos x 2cos x 2 

 

tan x cot x sin 2x cos2x   3cos x 4sin x cos x sin x 04 2

  

3

4cos x 2sin x 3sin x 0   cos x 4sin x 3cos x sin x sin x 03    

3

cos x sin x cos x sin x   sin x 3sin x cos x 02   

3

cos x sin x 3sin x cos x 0  

3 2

4sin x 3cos x 3sin x sin x cos x 0   

3

2cos x sin 3x

 

2

2sin x 6sin x cos x 1   3 cos x 5  3 0

1) 3cos3xsin3x ;2,cos7xcos5x 3sin2x sin7xsin5x

3;Tìm nghiÖm x ) ; (  

 cña PT:cos7x 3sin7x

4) 2(sinxcosx)cosx3cos2x;

PT đcấp bậc sin cos Bài Giải cỏc phương trỡnh.(Dạng: asinx + bcosx = c)

3 sin 3x cos3x

2

  3sin 5x 2cos5x 3  sin x 3 cos x 1

4sin x cos x 4  sin 2x cos 2x 1 

   

sin x sin x cos x cos x 1

3 sin 3x cos3x  2 sin x sin 2x 3cos x2   sin x cos x 2 sin x cos x 

 

sin8x cos6x  3 sin 6x cos8x

1 sin 2x

2

 với 0 x   cos x 3

3 2



 

 

 

  với

x     

 0

tan 2x 15 1 với 1800 x 900

   cot 3x 13 với x 0

2 

  

1) sin2x + 2sinxcosx + 3cos2x - = ;2) sin2x – 3sinxcosx + = 0 3) 3sinxcosx + 4cos2x = 2sin2x + 5/2

4) )

2 cos( ) sin( ) ( sin

3   x   x  x ) 0

2 ( sin

5  

  x

5)[§HAN_98]a

x x

x

cos cos

sin

3   ;b

x x

x

cos cos

6 sin

4  

6) cos2x – 3sinxcosx – 2sin2x – = 0 7) 6sin2x + sinxcosx – cos2x = 2

PTLG Đxứng sin2n cos2n

Bài 11 Giải phương trình (Dạng đối xứng phản đối xứng)

 

2 sin x cos x 6sin x cos x 0  sin x cos x 4sin x cos x 0   

 

sin x cos x 2 sin x cos x  1 0 6 sin x cos x   1 sin x cos x sin x cos x sin x cos x  2 sin x cos x   3sin 2x

 

2sin 2x 3 sin x cos x   8 0 sin x 2sin 2x 1 cos x

2

  

1)[§HBKHN_96] sin4x + cos4x = cos2x;2)[§H HuÕ_99] sin6x + cos6x = 7/16 3) sin6x + cos6x = sin 2x

4

1 ;4) sin6x + cos6x = cos4x 5)[HVCTQG TPHCM_00]:16(sin6x + cos6x – 1) + 3sin6x = 0 6)[§HQG_98] cos6x – sin6x =

8 13

cos22x;7)[§HC§_01] x x) 1 2sinx

( cos ) (

sin4   

sư dơng ct h¹ bËc

Bài 12 Giải phương trình

2 2 3

cos x cos 2x cos 3x 2

   sin x sin 2x sin 3x2 2 3

2

  

cos x cos 2x cos3x cos 4x 0    sin 3x sin x sin 2x 0   cos11x.cos3x cos17x cos9x sin18x.cos13x sin 9x.cos 4x

1 sin2 x sin 32 x cos 22 x cos 42 x

   sin2 xsin 22 x sin 32 x0

2 sin2 sin 22 sin 32

x x x 4; sin8 cos8 17cos 22 16

x x x

5) cos2x + cos22x + cos23x = 3/2;6) cos2x + cos22x + cos23x = 1

7)[§H HuÕ] sin2x + sin22x + sin23x = 3/2 ;8)[§HY_98] sin23x – sin22x – sin2x = 0 9)[§HQG_98] sin2x = cos22x + cos23x

10)[§H_B02]sin23x – cos24x = sin25x – cos26x ;11)cos2x + cos22x + cos23x + cos24x = 2 12) cos2x + cos22x + cos23x + cos24x = 3/2

Phơng trình bin i v tớch

Bài 13 : Giải phơng trình

1 cosxcos 2xcos3xcos 4x0 ;2 cosxcos3x2 cos5x0

3) sinx + sin2x + sin3x = + cosx + cos2x ;4) sinx + sin2x + sin3x = cosx + cos2x + cos3x 5)[ĐH Nông Lâm TPHCM_01]:1 + cosx + cos2x + cos3x =

6)[HVQHQT_99] cosx + cos2x + cos3x + cos4x =

8)[ĐH Đà Nẵng_B97] sin3x sinx + sin2x =

7) cos10x – cos8x – cos6x + = ;8)[HVQHQT_00] cosx + cos3x + 2cos5x = 9)[§HNTHN_97] 9sinx + 6cosx – 3sin2x + cos2x =

10)[§HNT TPHCM_00]1 + sinx + cos3x = cosx + sin2x + cos2x 12) (2sinx – 1)(2sin2x + 1) = – 4cos2x

13)[§HYHN_96] (cosx – sinx)cosxsinx = cosxcos2x

14)[§HHH_00] (2sinx + 1)(3cos4x + 2sinx 4) + 4cos2-x = 15)[ĐH Đà N½ng_99] cos3x – sin3x = sinx – cosx

16)[ĐH Thuỷ Sản Nha Trang_96] cos3x + sin3x = sinx – cosx 17)[§HCSND_00] cos3x + sin3x = sin2x + sinx +cosx

18)[HVQY_00] cos2x + sin3x + cosx = 0 19)[HVNH_99] cos3x + cos2x + 2sinx – = 0 20)[HVNH TPHCM_00] sinx + sin2x + cos3x = 0 21)[HVBCVT TPHCM_97] cos2x – 4sinxcosx = 0

sd CT biến đổi tích thành tổng

1) cos11x.cos3x = cos17x.cos9x 2) sin18x.cos13x = sin9x.cos4x