Chuyen de Phuong trinh luong giac

ph¬ng tr×nh lîng gi¸c

vÒ ptlg c¬ b¶n, ptlg gÇn c¬ b¶n

vÒ pt bËc nhÊt ®èi víi sinx vµ cosx

Bµi 1: Gi¶i ph¬ng tr×nh lîng gi¸c

1) cos(x-2) = - cos(5x+2)

2) tanx = cot(x+60o

), x∈(0o

; 270o

)

3) sinx

2

= cosx

2

4) cos(x

2

-x) = sin(x-π/2)

5) tan3x + cot2x = 0

6) tan(πcosx) = tan(2πcosx), x∈[0

o

; 360o

)

7*) sin(cosx) = cos(sinx)

Bµi 2: Gi¶i ph¬ng tr×nh lîng gi¸c

1)  cos(2x+1)= 1/2

2) tan2

x = cot2

x, x∈(0; 7π)

3) sin2

(6x-π/3) + cos2

(x+π) = 1

4*) cot3x.tan2x = 1

Bµi 3: Gi¶i vµ BL ph¬ng tr×nh

1) sin2

x + (2m-1)cos2

(x+π) = m

2) m(tanx + cotx) = 2cotx ##

Bµi 4: Gi¶i ph¬ng tr×nh lîng gi¸c

1) sinx - cosx =

2

1+ 3

, x∈(0; 2π)

2) sin2

x - 2sinxcosx = 5

3) 2sin25x +(3+ 3 )sin5xcos5x +

+ ( 3 -1) cos25x = -1

4) 3 cos4x - 2sin2xcos2x = 2

5) 3 (cos4x + sin3x) = cos3x – sin4x

6) 2- tanx = 2/ cosx

Bµi 2: T×m m ®Ó ph¬ng tr×nh sau cã

nghiÖm (2m-1)sinx + (m-1)cosx = m-3

Bµi 3: Cho PT mcos2x + sin2x = 2

1. GPT víi m = 2

2. m = ? PT cã nghiÖm.

Bµi 4: Gi¶i vµ BL ph¬ng tr×nh

msin(x/3) + (m+2)cos(x/3) = 2

Bµi 5: T×m GTLN, GTNN cña hµm sè

x x

x

y

2 cos sin

2 cos

+ −

+

=

Bµi 6: T×m m ®Ó mäi nghiÖm cña ph¬ng tr×nh

sinx + mcosx = 1

®Òu lµ nghiÖm cña ph¬ng tr×nh

msinx + cosx = m

2 ##

®¹i sè ho¸ ptlg

Bµi 1: Gi¶i ph¬ng tr×nh lîng gi¸c

1) sin2

x + 3 cos2

x + 3 cosxsinx = -

2

1

sin2x

2) 2 2 sin2

x - 3 sin2x = 2 - 6

3) 2sin2x + sin 2x =-1

4) cosx + sinx - 4sin3

x = 0

5) sinx(2cosx + sinx) = 2cos2

x +1/2

6) 5sinx – 2 = 3(1- sinx)tan2

x

Bµi 2: Gi¶i ph¬ng tr×nh lîng gi¸c

1) cos2xsin2

x + 1 = 0

2) 2- tan2

x = 2/ cos2

x

3) 4(tanx + cotx) + 3(tan2

x + cot2

x)=-2

4) tan2x - tanx = 0,5sin2x

5) tan2x + cotx = 4cos2

x

6) tan(x+π/4) = 1+ sin2x

7) tanx +tan2

x+ tan3

x +cotx +cot2

x+ cot3

x =6

8) 2 tan 1

1 cos 2

1 cos 2

= −

+

−

x

x

x

Bµi 3: Gi¶i ph¬ng tr×nh lîng gi¸c

1) 1+ sin2x = cosx + sinx

2) 1+ cosx + sinx + cos2x + sin2x = 0

4) sin3

x - cos3

x = cos2x

5) sin3

x + cos3

x = cosx + sinx+ sin2x

6)  cosx - sinx + 4sin2x = 1

7) tanx+cotx+cosx+sinx = - 2 -

x sin x

1

cos

1

−

Bµi 4: Gi¶i ph¬ng tr×nh lîng gi¸c

1) 3sin3x - 3 cos9x = 1+ 4sin33x

2) 8cos4

x = 3+5 cos4x

3) 











+ = − + + 2

sin

2

sin

sin

4

sin 2

2

x

x

x

x

4) 2cos2

(6x/5) + 1 = 3cos(8x/5)

5) 6

3cos 4sin 1

6

3cos 4sin =

+ +

+ +

x x

x x

6) sin4

x +(1+ sinx)

4 = 17

PTCB §K cã nghiÖm NghiÖm

sinx= m m≤ 1, sinx= sinα







= − +

= +

π α π

α π

2

2

x k

x k

cosx= m m≤ 1, cosx= cosα x = ±α + k2π

tanx= m ∀m, tanx= tanα x = α + kπ

cotx= m ∀m, cotx= cotα x = α + kπ

PTCB §K cã nghiÖm NghiÖm

sinx= m m≤ 1, sinx= sinα







= − +

= +

π α π

α π

2

2

x k

x k

cosx= m m≤ 1, cosx= cosα x = ±α + k2π

tanx= m ∀m, tanx= tanα x = α + kπ

cotx= m ∀m, cotx= cotα x = α + kπ

Cßn n÷a