PHƯƠNG TRÌNH LƯỢNG GIÁC Giải các phương trình sau: 1.
Trang 1PHƯƠNG TRÌNH LƯỢNG GIÁC Giải các phương trình sau:
1 4cos5x2 cos3x2 + 2(8sinx-1)cosx = 5 (D - 2010)
2 (sin2x+cos2x)cosx + 2cos2x - sinx = 0 (B - 2010)
x
x x x
cos 2
1 tan
1
4 sin ) 2 cos sin
1
(
(A - 2010)
4 3 cos5x - 2sin3xcos2x - sinx = 0 (D - 2009)
5 sinx + cosxsin2x+ 3cos3x = 2(cos4x+ sin3x) (B - 2009)
6 3
sin 1 sin
2
1
cos sin
2
1
x x
x x
(A - 2009)
7 2sinx(1+2cos2x)+ sin2x = 1 + 2cosx (D - 2008)
8 sin3x - 3cos3x = sinxcos2x - 3sin2xcosx (B - 2008)
x
7 sin 4 2
3 sin
1 sin
2
x
(D - 2007)
12 (1 + sin2x)cosx + (1 + cos2x)sinx = 1 + sin2x (A - 2007)
2 tan tan 1 sin
x x
0 sin
2 2
cos sin
sin cos
x x
x
x
(A - 2006)
16 cos4x + sin4x + cos
4
4
3x - 23 = 0 (D - 2005)
17 1 + sinx + cosx + sin2x + cos2x = 0 (B - 2005)
19 (2cosx - 1)(2sinx + cosx) = sin2x - sinx (D - 2004)
2
cos
tan 4
2
x
x
(D - 2003)
22 cotx - tanx + 4sin2x = sin22x (B - 2003)
Trang 223 cotx - 1= x x
x
x
2 sin 2
1 2 sin tan
1
2 cos
25 sin23x - cos24x = sin25x - cos26x (B - 2002)
2 sin 2 1
3 sin 3 cos
x
x x
27 2sin2x - cos2x = 7sinx + 2cosx - 4 (ĐHQGHN - 2001)
28 cos3xcos3x - sin3xsin3x = cos34x + 41 (ĐHNNHN - 2001)
30 sin4x + sin4(x + 4 ) + sin4 (x - 4 ) = 89 (ĐHGTVT - 2001)
31 48 -
x
x sin
2 1
-2001)
2
3 10
sin 2
1 2 10
(ĐHThủy lợi - 2001)
33 sin2x - cos2x = 3sinx +cosx - 2 (ĐHNN1 - 2001)
34 4sin3xcos3x + 4cos3xsin3x + 3 3cos4x = 3 (HVCNBCVVT - 2001)
35 tan2xcot22xcot3x = tan2x - cot22x + cot3x(ĐH Luật - 2001)
x 2 tan
sin
2 2
2
+ 5tanx + 5cotx + 4 = 0 (ĐH TM - 2001)
37 sin4 2
x
+ cos4 2
x
= 1 - 2sinx (ĐH Công đoàn - 2001)
4
2x + cos
4
2x + 4sinx = 2 + 2(1 - sinx) (ĐH Hàng hải - 2001)
39 sin2x + 2cos2x = 1 + sinx - 4cosx (ĐH An ninh 2001)
40 2cos2x + sin2xcosx + cos2xsinx = 2(sinx + cosx) (ĐHDL PĐ - 2001)
41 sin2x + sin22x + sin23x = 2 (ĐHSP TPHCM)
42 cos3x + 2 cos23 x
43 sin4x + cos4x = sin2x - 21
44 4sin3x + 4sin2x + 3sin2x + 6cosx = 0