MT S PHNG TRèNH LNG GIC THNG GP ! "#$%& !"#"$% &"'()*+%, -. -"/ 0"#$'(- !123142 5"#)*+,)%6789: ;84<,=>'3=,2 -./0123 *2'$4? -."/,'7 '$ @)=&(,'7$ *20'$4? -"/,'7 '$ @)%31 [ ] 0 A B A B C A CB4 5 6 75 6 4+ + = *25'$4? -."/D2D '$ @)%31 24 6 7 6 + = @+EF%> 0 G 0 0 @ 0 )!2 0 0 4 7+ 8"%"'(,'7$ *2H'$4? -6."/D2D '$ @)%31 0 0 2 24 6 7 6 6 6 )+ + = @ 0 GI-D2DJCFKLM GN-=2D C)!22 0 D"'7 0 C4 6 746 + + = ,'$4? -"/D *2OP'24?,'7F '$ @QRKS,'7"'(319 )ITUQVI*WUQXY II. PHNG TRèNH BC HAI I VI MT HM S LNG GIC I!"Z 2 sin sin : 0 1.t x hoaởc t x thỡ ủieu kieọ n t= = Baứi 1. '$4? B0 0 DGO2DGJC 0BH 0 D[H2D[JC 5BH2 O DD[H O D2DJ 0 HD HB ( ) 2 tan 1 3 tan 3 0x x+ = OB ( ) 2 4sin 2 3 1 sin 3 0x x + + = \B 3 4cos 3 2 sin2 8cosx x x+ = "829:;<=><?;;<? Q1 +Z +(F> 2 sin 0asin x b x c+ + = JD 1 1t 2 cos cos 0a x b x c+ + = J2D 1 1t 2 tan tan 0a x b x c+ + = JD ( ) 2 x k k Z + 2 cot cot 0a x b x c+ + = J2D ( )x k k Z  ]B 0 DG2 0 DJ0 ^B2 0 0D[H20DG5JC Baøi 2. '$4? BH 0 5DG ( ) 2 3 1 cos3 3x+ − JH 0B20DG_2DGOJC 5BH2 0 A0[\DBG\2 0 A[5DBJ5 HB ( ) 2 1 3 3 tan 3 3 0 cos x x − + − + = OB 3 cos x G 0 DJ_ \B_[52DG 2 4 1 tan x+ JC ]B 2 1 sin x J2DG5 ^B 2 1 cos x G52 0 DJO _B20D[52DJ 2 4cos 2 x CB020DGDJ 4 5 Baøi 3. )2'$4? sin3 cos3 3 cos2 sin 1 2sin2 5 x x x x x   + + + =  ÷ +   ?>`'$4? ( ) 0 ; 2 π  Baøi 4. )2'$4?2OD2DJ2HD20DG520DG?>`'$4?  ( ) ;− π π  Baøi 5. '$4? 4 4 4 5 sin sin sin 4 4 4 x x x     + + + − =  ÷  ÷     π π  III. PHƯƠNG TRÌNH BẬC NHẤT THEO SINX VÀ COSX DẠNG: a sinx + b cosx = c (1) Cách 1: • )!'$4?2 2 2 a b+ "'7 AB⇔ 2 2 2 2 2 2 sin cos a b c x x a b a b a b + = + + + • +Z ( ) 2 2 2 2 sin , cos 0, 2 a b a b a b   = = ∈   + + α α α π  '$4?4a 2 2 sin .sin cos .cos c x x a b + = + α α 2 2 cos( ) cos (2) c x a b ⇔ − = = + α β • +(F>"&'$4?%>, 2 2 2 2 2 1 . c a b c a b ≤ ⇔ + ≥ + • A0B 2 ( )x k k Z⇔ = ± + ∈ α β π Cách 2: E b 2 2 2 x x k k= + ⇔ = + π π π π %,>=FKc E b 2 cos 0. 2 x x k≠ + ⇔ ≠ π π "829:;<=><?;;<?  +Z 2 2 2 2 1 tan , sin , cos , 2 1 1 x t t t thay x x t t − = = = + + "'7'$4? -d2 2 ( ) 2 0 (3)b c t at c b+ − + − = N? 2 0,x k b c≠ + ⇔ + ≠ π π eA5B%>F 2 2 2 2 2 2 ' ( ) 0 .a c b a b c= − − ≥ ⇔ + ≥ ∆ A5B8/f> C 8%'$4? 0 tan . 2 x t= Ghi chú: E )0'g3R"& >,- 0E )23R=0?"(F>"&'$4?%> 2 2 2 .a b c+ ≥ 5E *."hS*) 2 2 2 2 2 2 .sin .cos . sin cosy a x b x a b x x a b= + ≤ + + = + 2 2 2 2 sin cos min max tan x x a y a b vaø y a b x a b b ⇔ = − + = + ⇔ = ⇔ = Baøi 1. '$4? B cos 3sin 2x x+ = 0B 6 sin cos 2 x x+ = 5B 3 cos3 sin3 2x x+ = HB sin cos 2 sin5x x x+ = OB ( ) ( ) 3 1 sin 3 1 cos 3 1 0x x− − + + − = \B 3sin2 sin 2 1 2 x x   + + =  ÷   π Baøi 2. '$4? B 2 2sin 3 sin2 3x x+ =  0B ( ) sin8 cos6 3 sin6 cos8x x x x− = +  5B 3 1 8cos sin cos x x x = +  HB2D[ 3sin 2cos 3 x x   = −  ÷   π OBODG2ODJ 2 25D \BA52D[HD[\B 0 G0J[5A52D[HD[\B Baøi 3. '$4? B5D[02DJ0 0B 3 2DGHD[ 3 JC 5B2DGHDJ[ HB0D[O2DJO Baøi 4. '$4? B0 4 x   +  ÷   π G 4 x   −  ÷   π J 3 2 2 0B 3 cos2 sin2 2sin 2 2 2 6 x x x   + + − =  ÷   π Baøi 5. ?"&'$4?AG0BDG2DJ0%> Baøi 6. ?"&'$4?A0[BDGA[B2DJ[5K> IV. PHƯƠNG TRÌNH ĐẲNG CẤP BẬC HAI DẠNG: a sin 2 x + b sinx.cosx + c cos 2 x = d (1) Cách 1: • i&42DJC%2M=FKc @*A2DJC 2 sin 1 sin 1. 2 x k x x⇔ = + ⇔ = ⇔ =± π π • i cos 0x ≠ 8!'$4?AB2 2 cos 0x ≠ "'7 "829:;<=><?;;<?  2 2 .tan .tan (1 tan )a x b x c d x+ + = + • +ZJD8"'('$4? -d2 2 ( ) . 0a d t b t c d− + + − =  Cách 2:QRKS1 - 1 cos2 sin2 1 cos2 (1) . . . 2 2 2 x x x a b c d − + ⇔ + + = .sin2 ( ).cos2 2b x c a x d a c⇔ + − = − − A"j=,'$4? -."/0D 20DB Baøi 1. '$4? B ( ) ( ) 2 2 2sin 1 3 sin .cos 1 3 cos 1x x x x+ − + − = 0B ( ) 2 2 3sin 8sin .cos 8 3 9 cos 0x x x x+ + − = 5B 2 2 4sin 3 3sin .cos 2cos 4x x x x+ − =  HB 2 2 1 sin sin2 2cos 2 x x x+ − = OB ( ) ( ) 2 2 2sin 3 3 sin .cos 3 1 cos 1x x x x+ + − = − \B 2 2 5sin 2 3sin .cos 3cos 2x x x x+ + = ]B 2 2 3sin 8sin .cos 4cos 0x x x x+ + =  ^B ( ) ( ) 2 2 2 1 sin sin2 2 1 cos 2x x x− + + + = _B ( ) ( ) 2 2 3 1 sin 2 3 sin .cos 3 1 cos 0x x x x+ − + − =  CB 4 2 2 4 3cos 4sin cos sin 0x x x x− + = B2 0 DG5 0 DG 2 3 D2D[JC 0B02 0 D[5D2DG 0 DJC Baøi 2. '$4? B 5 DG0 0 D2 0 D[52 5 DJC 0B 2 2 1 3sin .cos sin 2 x x x − − = Baøi 3. ?"&'$4?AGB 0 D[0DG02 0 DJ%> Baøi 4. ?"&'$4?A5[0B 0 D[AO[0B0DG5A0GB2 0 DJCK > "829:;<=><?;;<? . '$4? 4 4 4 5 sin sin sin 4 4 4 x x x     + + + − =  ÷  ÷     π π  III. PHƯƠNG TRÌNH BẬC NHẤT THEO SINX VÀ COSX DẠNG: a sinx + b cosx = c (1) Cách 1: • )!'$4?2 2. 6. ?"&'$4?A0[BDGA[B2DJ[5K> IV. PHƯƠNG TRÌNH ĐẲNG CẤP BẬC HAI DẠNG: a sin 2 x + b sinx.cosx + c cos 2 x = d (1) Cách 1: • i&42DJC%2M=FKc @*A2DJC 2 sin