x k x n x m
4) 4(sin3x cos2x) = 5(sinx 1) ĐS: 2 ; 2 ; 2 ;
2
x k x n x l
với sin 1
4
5) sinx 4sin3x + cosx = 0 (ĐH Y Hà Nội) ĐS:
4
x k
.
HD: sin3x - sin2x + cosx = 0; 3sinx - 4sin3x - 2sinxcosx + cosx = 0 (chia cho cosx)
6) sin 3 sin 2 .sin
4 4 x x x ; (Học Viện BCVT) ĐS: 4 2 x k Đổi sin(x+ 4 ) thanh cos( 2
- x) råi dïng công thức biÕn tÝch thµnh tæng.
7) sin3x.cos3x + cos3x.sin3x = sin34x
HD: sin2x.sinx.cos3x + cos2x.cosx.sin3x = sin34x ĐS:
12
xk
.
8) 3 3 2 2
sin x 3 cos xsin cosx x 3 sin xcosx
HD: Chia hai vế cho cos3x ĐS:x =
3 k
,
4
x k
9) 2sinx(1 + cos2x) + sin2x = 1 + 2cosx
HD: Đưa về cung x rồi đặt thừa số ĐS: 2 2 ( )
4 3
x k x k k
10) sin2x + cos2x = 1 + sinx – 3cosx (1).
HD: (1) 2sinxcosx+2cos2x–1=1+sinx–3cosx. 2cos2x+(2sinxcosx+3cosx)–sinx–2=0.
2cos2x + (2sinx + 3)cosx – (sinx + 2) = 0 cos 1 2
x
11) 1 + sinx + cosx + sin2x + 2cos2x = 0.
HD: (1+sin2x)+(sinx+cosx)+2cos2x = 0. (sinx+cosx)2+(sinx+cosx)+2(cos2x–sin2
x) = 0. (sinx+cosx)2+(sinx+cosx)+2(sinx+cosx)(sinx–cosx)=0. Đặt thừa số, giải tiếp …
12) 1 2 cos sin
tan cot 2 cot 1
x x x x x ĐS: 2 4 x k k
13) cos3xcos3x – sin3xsin3x = 2 3 2
8
HD: Ta có: cos3xcos3x – sin3xsin3x = 2 3 2
8 cos 4 2 , 2 16 2 x x k kZ .
HD: Phương trình (cosx – sinx)2– 4(cosx – sinx) – 5 = 0
15) (cosx + 1)(cos2x – mcox) = msin2x khi m = -2 (ĐH QG TP HCM)
16) sin2008x + cos2008x = 1
17) sin2x + sin23x = cos22x + cos24x (ĐHKTQD HN)
18) (ĐH HUẾ) a) sin4x + cos4x = cos4x b) sin6x + cos6x = 7 16
19)
10 10 6 6
2 2
sin cos sin cos 4 4sin 2 cos 2 x x x x x x 20) a) sin 3 1sin 3 10 2 2 10 2 x x b) cos4x cos x2 3 = 0
Bài 2: Giải các phƣơng trình:
1) sin2 x + sin23x = cos22x + cos24x 2) cos2x + cos22x + cos23x + cos24x = 3 2
3) sin2x + sin23x - 3cos22x = 0 4) cos3x + sin7x = 2sin2(π 5x +
4 2 ) - 2cos
29 2
x
5) cos4x - 5sin4x = 1 6) 4sin3x - 1 = 3 - 3cos3x 7) sin22x + sin24x = sin26x 8) sin2x = cos22x + cos23x
9) (sin22x + cos42x - 1): sinxcosx= 0 10) 2cos22x + cos2x = 4 sin22xcos2x 11) sin3xcos3x +cos3xsin3x=sin34x 12) 8cos3(x + π
3) = cos3x
13) sin5x
5sinx = 1 14) cos7x + sin 2
2x = cos22x - cosx 15) sin2x + sin22x + sin23x = 3/2 16) 3cos4x – 2cos23x =1
17) sin24x+ sin23x= cos22x+ cos2x víix (0; π)
18) sin24x - cos26x = sin(10,5π +10x) víi π x (0; )
2
19) 4sin3xcos3x + 4cos3x sin3x + 3 3cos4x = 3 20) cos4xsinx - sin22x = 4sin2(
4 2
x
) - 7
2 víi x -1 < 3
21) 2cos32x - 4cos3xcos3x + cos6x - 4sin3xsin3x = 0 22) cos10x + 2cos24x + 6cos3xcosx = cosx + 8cosxcos23x