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Phng trnh bc hai i vi mt hm s lng gic Dng : asin2x +bsinx + c = 0 , acos2x +bcosx + c = 0 , atan2x + btanx +c = 0 Cch gii : t t = sinx , cosx ( -1  EMBED Equation.3  t  EMBED Equation.3 1) hoc t = tan x Bi tp : 1.Gii cc phng trnh sau : a.2cos2x  sinx  1 = 0 b. 2sin22x  cos2x  1 = 0 c.cos2x + 9cosx +5 = 0 d.cos4x +7sin2x  6 = 0 e. cos6x  7cos3x + 4 = 0 f. cos4x +2cos2x  3 = 0 2. Gii cc phng trnh lng gic sau a. 4sin4x +12cos2x = 7 b.2cos4x + 3sin2x  2 = 0 c. 2sin4x = cos2x + 3 d. 4sin4x + 3cos2x = 1 3. Gii cc phng trnh lng gic sau : a. 2cos22x + 6sin2x  1 =0 b. 2cos22x  6cos2x + 5 = 0 c. sin3xsinx + cos2x  1 = 0 d.. cos4x + 14cos2x  3 = 0 e..cos3xcosx  2cos2x +1 = 0 2. Phng trnh bc nht i vi sinx v cosx : Dng : asinx +bcosx = c (1) Cch gii : Chia v cho  EMBED Equation.3 . Khi  ( 1)  EMBED Equation.3 sin(x+ EMBED Equation.3 ) =  EMBED Equation.3  Bi tp: 1. Gii cc phng trnh sau a. sinx + EMBED Equation.3 cosx = 2 b.cos2x +sin2x = 1 c.  EMBED Equation.3 cos4x  (sin2x +cos2x)2 = 0 d. 2cos2x +  EMBED Equation.3 sin2x = 3 2. Gii cc phng trnh sau : a.  EMBED Equation.3 (cosx  sinx)(cosx+sinx) + 2sinxcosx = 1 b.  EMBED Equation.3 cosx + sinx = 2cos2x c. 2cos6x +2cos4x -  EMBED Equation.DSMT4 cos2x = sin2x +  EMBED Equation.DSMT4  d.  EMBED Equation.DSMT4 (2cos2x +cosx  2 ) + (3  2cosx)sinx = 0 e. 2cos2x +2 EMBED Equation.DSMT4 sinxcosx + 1 = 3sinx +3 EMBED Equation.DSMT4 cosx 3. Phng trnh ng cp i vi sinx v cosx : Dng :asin2x +bsinxcosx+ccos2x = 0 ( a, b , c khc 0 ) Cch gii :cosx = 0 khng tha phng trnh nn chia hai v cho cos2x Khi  ta c phng trnh ; atan2x +btanx + c = 0 Bi tp : 1. Gii cc phng trnh sau : a.  EMBED Equation.DSMT4 sin2 x  ( EMBED Equation.DSMT4 +1)sinxcosx + cos2x = 0 b. 2sin22x + 3sin4x  8cos22x = 0 2. Gii cc phng trnh sau : a. 6sin2x +sinxcosx  cos2x = 3 b. 2cos3x +sinx  3sin2xcosx = 0 c.sin2x +  EMBED Equation.DSMT4 sinxcosx + 2cos2x = 1 d. 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(2sinx  1)(2sin2x +1) = 3  4cos2x Gii : (2sinx  1)(2sin2x +1) = 3  4cos2x  EMBED Equation.DSMT4 (2sinx  1)(2sin2x +1) = 3  4(1- sin2x)  EMBED Equation.DSMT4  (2sinx  1)(2sin2x +1) = 4sin2x  1  EMBED Equation.DSMT4 (2sinx  1)(2sin2x + 1) = (2sinx  1)(2sinx + 1)  EMBED Equation.DSMT4  EMBED Equation.DSMT4  a. 2sinx  1 = 0 ( gii tip) b.2sin2x + 1 = 2sinx + 1  EMBED Equation.DSMT4 sin2x = sinx  EMBED Equation.DSMT4 2sinxcosx  sinx = 0  EMBED Equation.DSMT4 sinx(2cosx  1) = 0 (gii tip) V d 2:Gii phng trnh sau :  EMBED Equation.DSMT4  Gii : k : 2cosx  1  EMBED Equation.DSMT4 0  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Ta c (1)  EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 . So vi iu kin ta nhn  EMBED Equation.DSMT4  V d 3: Gii phng trnh sau :sin23x  cos24x = sin25x  cos26x Gii : (1)  EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4 cos6x +cos8x = cos10x +cos12x  EMBED Equation.DSMT4 2cos7xcosx = 2cos11xcosx  EMBED Equation.DSMT4  EMBED Equation.DSMT4 (gii tip) Bi tp Bi 1:Gii cc phng trnh sau : a.  EMBED Equation.3  b.. EMBED Equation.DSMT4  c. tan2x =  EMBED Equation.DSMT4  d. 2cos3x + cos2x + sinx = 0 Bi 2 : Gii cc phng trnh sau : a. cotx  1 =  EMBED Equation.DSMT4  b.cotx  tanx +4sin2x =  EMBED Equation.DSMT4  c. 5sinx  2 = 3(1  sinx)tan2x d. (2cosx  1)(2sinx +cosx) = sin2x  sinx e. 3sinx + 2cosx = 2 + 3tanx f.  EMBED Equation.DSMT4  . Bi 3 :Gii cc phng trnh sau : a.cos2x +cosx (2tan2x  1) = 2 b.3  tanx(tanx +2sinx) + 6cosx = 0 c. EMBED Equation.DSMT4  d.tan4x + 1 =  EMBED Equation.DSMT4  e.tanx +cosx  cos2 x = sinx(1+tanx.tan EMBED Equation.DSMT4 ) f. EMBED Equation.DSMT4  Bi 4 :Gii cc phng trnh sau : a. cotx = tanx + EMBED Equation.DSMT4  b. cos2x +2sinx  1  2sinxcos2x = 0 f.  EMBED Equation.DSMT4  Bi 5 :Gii cc phng trnh sau a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  ( khi A-2009) c. . sinx + cosxsin2x + EMBED Equation.DSMT4 cos3x = 2(cos4x + sin3x) (khi B-2009) d..  EMBED Equation.DSMT4 cos5x  2sin3x.cos2x  sinx = 0 (khi D -2009) e. . ( 1+2sinx)2 cosx = 1 +sinx +cosx f . 2sin22x + sin7x  1 = sinx g. 2sinx(1+cos2x) + sin2x = 1 +2cosx h. sin3x -  EMBED Equation.DSMT4 cos3x = 2sin2x k. sin3x + cos3x = cos2x(2cosx  sinx) Bi 6 : Gii cc phng trnh sau : a.  EMBED Equation.DSMT4  b .  EMBED Equation.DSMT4  c.  EMBED Equation.DSMT4  d. 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