mot so bai tap ve phuong trinh luong giac hay 75949

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Bài 1 : Giải các phương trình sau
1. cos2x + 3sin x = 2 ;2. 4sin4 x + 12cos2 x = 7; 3. 25sin2 x + 100cos x = 89
4. sin 2x + cos 2x = sin2xcos2x
4

4

sin6 x + cos6 x 1
= tan2x
;5. 2
cos x − sin2 x 4

3
= 9 ,7,2sin2x – cos2x - 4sinx + 2 = 0;8,9cos2x - 5sin2x - 5cosx + 4 = 0
cos x
π
π
9) 5sinx(sinx - 1) - cos2x = 3;10)cos2(3x + ) – cos23x – 3cos( - 3x) + 2 = 0
2
2
2
11;cos2x + sin x + 2cosx + 1 = 0;12; 3cos2x + 2(1 + 2 + sinx)sinx – (3 + 2 ) = 0
3
13, tg2x + ( 3 - 1)tgx – 3 = 0;14) 2 = 3 cot gx + 3
sin x
2
2
4 sin 2 x + 6 sin x − 9 − 3 cos 2 x
cos x(cos x + 2 sin x ) + 3 sin x(sin x + 2 )

15;
= 0 ;16;
=1
cos x
sin 2 x − 1
Bai 2Chuyên Đề PT bậc nhất đối với Sin và cos
1)
3 cos 3x + sin 3x = 2 ;2, cos 7 x cos 5 x − 3 sin 2 x = 1 − sin 7 x sin 5 x
2π 6π
3;Tìm các nghiệm x ∈ ( ; ) của PT: cos 7 x − 3 sin 7 x = − 2
5 7
4) 2 2 (sin x + cos x) cos x = 3 + cos 2 x ;
Bai 3:Chuyên Đề : PT đcấp bậc 2 đối với sin và cos
1) sin2x + 2sinxcosx + 3cos2x - 3 = 0 ;2) sin2x – 3sinxcosx + 1 = 0
3) 4 3 sinxcosx + 4cos2x = 2sin2x + 5/2
5π
π
3π
2
+ x) cos( + x) − 5 sin 2 ( + x ) = 0
4) 3 sin (3π − x) + 2 sin(
2
2
2
1
1
5)[ĐHAN_98]a. 3 sin x + cos x =
;b. 4 sin x + 6 cos x =
cos x
cos x

2
2
6) cos x – 3sinxcosx – 2sin x – 1 = 0
7) 6sin2x + sinxcosx – cos2x = 2
Bai 4:Chuyên Đề 8: PTLG Đxứng đối với sin2n và cos2n
1)[ĐHBKHN_96] sin4x + cos4x = cos2x;2)[ĐH Huế_99] sin6x + cos6x = 7/16
1 2
3) sin6x + cos6x = sin 2 x ;4)
sin6x + cos6x = cos4x
4
5)[HVCTQG TPHCM_00]:16(sin6x + cos6x – 1) + 3sin6x = 0
13
4 x
4 x
6)[ĐHQG_98] cos6x – sin6x =
cos22x;7)[ĐHCĐ_01] sin ( ) + cos ( ) = 1 − 2 sin x
8
2
2
Bai 5: Chuyên Đề 9: sử dụng ct hạ bậc
1. sin 2 x + sin 2 3 x = cos 2 2 x + cos 2 4 x
3. sin 2 x + sin 2 2 x − sin 2 3 x = 0
3
17
2. sin 2 x + sin 2 2 x + sin 2 3 x =
4; . sin 8 x + cos8 x = cos 2 2 x
2
16
5) cos2x + cos22x + cos23x = 3/2;6)cos2x + cos22x + cos23x = 1
7)[ĐH Huế] sin2x + sin22x + sin23x = 3/2 ;8)[ĐHY_98] sin23x – sin22x – sin2x = 0

9)[ĐHQG_98] sin2x = cos22x + cos23x
10)[ĐH_B02]sin23x – cos24x = sin25x – cos26x ;11)cos2x + cos22x + cos23x + cos24x = 2
12) cos2x + cos22x + cos23x + cos24x = 3/2

6. tan2 x +

C – Phương trình biến đổi về tích


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Bài 6 : Giải phương trình
1 . cos x + cos 2 x + cos 3 x + cos 4 x = 0 ;2. cos x + cos 3 x + 2 cos 5 x = 0
3) sinx + sin2x + sin3x = 1 + cosx + cos2x ;4)
sinx + sin2x + sin3x = cosx + cos2x + cos3x
5)[ĐH Nông Lâm TPHCM_01]:1 + cosx + cos2x + cos3x = 0
6)[HVQHQT_99] cosx + cos2x + cos3x + cos4x = 0
7)[ĐHSP Vinh_97] sinx + sin2x + sin3x + sin4x + sin5x + sin6x = 0
8)[ĐH Đà Nẵng_B97] sin3x – sinx + sin2x = 0
7) cos10x – cos8x – cos6x + 1 = 0 ;8)[HVQHQT_00] cosx + cos3x + 2cos5x = 0
9)[ĐHNTHN_97] 9sinx + 6cosx – 3sin2x + cos2x = 8
10)[ĐHNT TPHCM_00]1 + sinx + cos3x = cosx + sin2x + cos2x
12) (2sinx – 1)(2sin2x + 1) = 3 – 4cos2x
13)[ĐHYHN_96] (cosx – sinx)cosxsinx = cosxcos2x
14)[ĐHHH_00] (2sinx + 1)(3cos4x + 2sinx – 4) + 4cos2-x = 3
15)[ĐH Đà Nẵng_99] cos3x – sin3x = sinx – cosx
16)[ĐH Thuỷ Sản Nha Trang_96] cos3x + sin3x = sinx – cosx
17)[ĐHCSND_00] cos3x + sin3x = sin2x + sinx +cosx
18)[HVQY_00] cos2x + sin3x + cosx = 0
19)[HVNH_99] cos3x + cos2x + 2sinx – 2 = 0

20)[HVNH TPHCM_00] sinx + sin2x + cos3x = 0
21)[HVBCVT TPHCM_97] cos2x – 4sinxcosx = 0
Chuyên Đề 13: sd CT biến đổi tích thành tổng
1) cos11x.cos3x = cos17x.cos9x
2) sin18x.cos13x = sin9x.cos4x
3) sin2x + sin2xsin4x + sin3xsin9x + sin4xsin16x = 1
4) (sinx + 3 cosx)sin3x = 2