81 bai tap PTLG du dang.

Ph¬ng tr×nh lîng gi¸c-PDT 1/. T×m x∈ (0; 2π) cña pt : 32 221 33 5 +=       + + + xcos xsin xsinxcos xsin 2/. sin 2 3x - cos 2 4x = sin 2 5x - cos 2 6x 3/. T×m x ∈ [0;14] : cos3x - 4cos2x + 3cosx - 4 = 0 . 4/. cosx+ cos2x + cos3x + cos4x + cos5x = -1/2 5/.(cos2x - 1)(sin2x + cosx + sinx) = sin 2 2x 6/.5sinx - 2 = 3(1 - sinx)tg 2 x 7/.cotgx - 1 = tgx xcos + 1 2 + sin 2 x - 2 1 sin2x 8/.cotgx - tgx + 4sin2x = xsin 2 2 9/. 0 242 222 =−       π − x cosxtg x sin 10/. 4 4 3 cos sin cos sin 3 0 4 4 2 x x x x π π     + + − − − =  ÷  ÷     10/. ( )( ) xsinxsinxcosxsinxcos −=+− 2212 12/. cos 2 3xcos2x - cos 2 x = 0 13/. 1 + sinx + cosx + sin2x + cos2x = 0 14/. cos3x + cos2x - cosx - 1 = 0 15/. ( ) 6 6 2 sin sin .cos 0 2 2sin cos x x x x x + − = − 16/.cotx + sinx(1+tanx.tanx/2) = 4 17/. ( ) ( ) 2 2 1 sin cos 1 cos sin 1 sin 2x x x x x+ + + = + 18/. 2sin 2 2x + sin7x - 1 = sinx 19/. 2 sin cos 3 cos 2 2 2 x x x   + + =  ÷   20/.T×m m: ( ) 02sin24coscossin4 44 =−+++ mxxxx cã Ýt nhÊt mét nghiÖm thuéc ®o¹n       2 ;0 π 21/. x xg x xx 2sin8 1 2cot 2 1 2sin5 cossin 44 −= + 22/. ( ) x xx xtg 4 2 4 cos 3sin2sin2 1 − =+ 23/. tgx + cosx - cos 2 x = sinx(1 + tgxtgx/2) 24/. x x sin cos8 1 2 = 25/. xsin xcos tgxgxcot 2 42 += 26/. ( ) 0623 =++− xcosxsintgxtgx 27/. cos2x + cosx(2tg 2 x - 1) = 2 29/. sin(πcosx) = 1 30/. 032943 26 =++− xcosxcosxcos 31/. xsinxcostgxxtg 3 3 1 2 =− 32/. 5 5 3 3 xsinxsin = 33/. ( ) ( ) 02122 3 =−+++−+ xcosxsinxsinxcosxsin 34/. 01 =++ xcosxsin 35/. ( ) 442 =−+ xsinxcosxsin 36/.Cho PT: a xx xx = +− ++ 3cos2sin 1cossin2 (2) (a lµ tham sè) a) Gi¶i a =1/3. b) T×m a ®Ó ph¬ng tr×nh (2) cã nghiÖm ? 37/.Cho ph¬ng tr×nh: ( ) 01122 =−+−+ mxcosmxcos 1) Gi¶i m = 1. 2) m=? ®Ó PT cã nghiÖm/       π π ; 2 . 38/. ( ) 1 1cos2 42 sin2cos32 2 = −       −−− x x x π 39/. ( ) ( ) xsin xcosxsin xcosxcos += + − 12 1 2 40/. xcos xcosxcos 1 7822 =+− 41/. 022 3 =−+ xcosxcosxsin 42/.Cho ph¬ng tr×nh: ( ) ( ) m tgxtgx =−++ 223223 1) Gi¶i m = 6. 2) m=? ®Ó PT cã ®óng 2 ng PB/       ππ − 22 ; . 43/. 0 239624 22 = −−+ xcos xcosxsinxsin 43/.A/. ( ) 1 2 2 1 − − = + gxcot xsinxcos xgcottgx 44/. 23sin2sinsin 222 =++ xxx 45/. 03sin2cos4cossin =+ xxxx 46/. 0221 =++++ xcosxsinxcosxsin 47/.tg2x + cotgx = 8cos 2 x 48/. xtg xsinxcos xcosxsin 2 8 13 22 66 = − + 49/.      π −= π − =+ 22 1 22 y y x x ysinxsin 50/. sinx.cosx + cosx = -2sin 2 x - sinx + 1 51/. sin3x = cosx.cos2x.(tg 2 x + tg2x) 52/. ( ) ( ) 1 12 232 = − +++ xsin xsinxsinxsinxcosxcos 53/.       = 33 4 2 x cos x cos 54/. ( ) 032332 =++−++ xcosxcosxcosxsinxsinxsin 55/. ( ) 1221 2 −=−− xsinxsinxcosxsin 56/. xsinxsin 2 4 3 =       π + 57/. ( ) 1 2 2 1 − − = + gxcot xsinxcos xgcottgx 58/. GBL: 2m(cosx + sinx) = 2m 2 + cosx - sinx + 3/2 59/. 1 20002000 =+ xcosxsin 60/.       + π =       − π 2 3 102 1 210 3 x sin x sin 61/. x x xx cos4 sin 2sin12sin1 = ++− 62/. cos2x + cos4x + cos6x = cosxcos2xcos3x + 2 63/. cosx + cos2x + cos3x + cos4x = 0 64/. sin 4 x + cos2x + 4cos 6 x = 0 65/. sinx + sin 2 x + sin 3 x + sin 4 x = cosx + cos 2 x + cos 3 x + cos 4 x 66/.sin 3 x.cos3x + cos 3 x.sin3x = sin 3 4x 67/. 2tgx + cotg2x = 2sin2x + 1/sin2x 68/. cosx.sinx + 1 =+ xsinxcos 69/.cos7x - 273 −= xsin tm: π<<π 7 6 5 2 x 70/.9sinx + 6cosx - 3sin2x + cos2x = 8 71/. 3(cotgx - cosx) - 5(tgx - sinx) = 2 72/. ( ) xsinxcosxcosxcos 4 2 1 21 =+− 73/. tgx + 2cotg2x = sin2x 74/.2cosxcos2x = 1 + cos2x + cos3x 75/. 3sinx + 2cosx = 2 + 3tgx 76/. sin 3 x.cos3x + cos 3 x.sin3x = sin 3 4x 77/       π +=       π − 4 2 4 3 xsin.xsinx 3 32 32 = ++ ++ xcosxcosxcos xsinxsinxsin 78/.T×m nghiÖm: sinxcos4x + 2sin 2 2x = 1 - 4       − π 24 2 x sin tm :    −>+ <− xx x 3 31 2 79/.(1 + tgx)(1 + sin2x) = 1 + tgx 80/.2sin 3 x - sinx = 2cos 3 x - cosx + cos2x 81/.sinx + cosx + cos2x - 2sinx.cosx = 0 . 79/.(1 + tgx)(1 + sin2x) = 1 + tgx 80/.2sin 3 x - sinx = 2cos 3 x - cosx + cos2x 81/ .sinx + cosx + cos2x - 2sinx.cosx = 0