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C6 phuongtrinhdangcap
- 1. CHNG VI: PHNG TRNH ANG CAP 2 2 asin u bsinu cosu ccos u d+ + = Ca湛ch gia短i : ( )T狸m nghie辰m u k lu湛c 単o湛 cosu 0 va淡 sinu 1 2 = + = = 賊 2 Chia hai ve叩 ph旦担ng tr狸nh cho cos u 0 ta 単旦担誰c ph旦担ng tr狸nh : ( )2 2 atg u btgu c d 1 tg u+ + = + a谷t ta co湛 ph旦担ng tr狸nh :t tgu= ( ) 2 a d t bt c d 0 + + = Gia短i ph旦担ng tr狸nh t狸m 単旦担誰c t = tgu Ba淡i 127 : Gia短i ph旦担ng tr狸nh ( )2 2 cos x 3 sin 2x 1 sin x * = + V狸 cosx = 0 kho但ng la淡 nghie辰m ne但n Chia hai ve叩 cu短a (*) cho 2 cos 0 ta 単旦担誰c ( ) ( )2 2 * 1 2 3tgx 1 tg x tg x = + + a谷t t = tgx ta co湛 ph旦担ng tr狸nh : 2 2t 2 3t 0+ = t 0 t 3 = = Va辰y ( )* = = = = + tgx 0 hay tgx 3 x k hay x k , k 3 Ba淡i 128 : Gia短i ph旦担ng tr狸nh ( )3 3 2 cos x 4 sin x 3cos x sin x sin x 0 * + = Khi x k th狸 cos x 0va淡 sin x 2 = + = = 賊1 th狸 (*) vo但 nghie辰m Do kho但ng la淡 nghie辰m ne但n chia hai ve叩 cu短a (*) cho cos3 x=cos x 0 ta co湛 (*) ( )3 2 2 1 4tg x 3tg x tgx 1 tg x 0 + + = ( )( ) + = + = = = 賊 = + = 賊 + 3 2 2 3tg x 3tg x tgx 1 0 tgx 1 3tg x 1 0 3 tgx 1 tgx 3 x k x k , k 4 6
- 2. Ba淡i 129 : Gia短i ph旦担ng tr狸nh ( )4 2 2 4 3cos x 4 sin x cos x sin x 0 * + = Do cosx = 0 kho但ng la淡 nghie辰m ne但n chia hai ve叩 cu短a (*) cho 4 cos x 0 Ta co湛 : (*) 2 4 3 4tg x tg x 0 + = = = = 賊 = 賊 = 賊 = 賊 + = 賊 + 2 2 tg x 1 tg x 3 tgx 1 tg tgx tg 4 3 x k x k , k 4 3 Ba淡i 130 : Gia短i ph旦担ng tr狸nh ( )sin 2x 2tgx 3 *+ = Chia hai ve叩 cu短a (*) cho 2 cos x 0 ta 単旦担誰c (*) 2 2 2sin x cos x 2tgx 3 cos x cos x cos x + = 2 ( ) ( )2 2 2tgx 2tgx 1 tg x 3 1 tg x + + = + 3 2 t tgx 2t 3t 4t 3 0 =ｧ ｨ + =ｩ ( )( ) =ｧｪ ｨ +ｪｩ 2 t tgx t 1 2t t 3 0= = = + tgx 1 x k , k 4 Ba淡i 131 : Gia短i ph旦担ng tr狸nh ( )3 sin x sin 2x sin 3x 6cos x *+ = ( ) 2 3 * 2sin x cos x 3sin x 4sin x 6cos x + = 3 ( ) = = 賊Khi cos x 0 ( sin x 1) th狸 * vo但 nghie辰m Chia hai ve叩 ph旦担ng tr狸nh (*) cho 3 cos x 0 ta 単旦担誰c ( )* 2 3 2 2 2sin x 3sin x 1 sin x . 4 cos x cos x cos x cos x + 3 6= ( ) ( )( ) + + = + = = = = 留 = 賊 = 留 + = 賊 + 留 = 2 2 3 3 2 2 2tg x 3tgx 1 tg x 4tg x 6 tg x 2tg x 3tgx 6 0 tgx 2 tg x 3 0 tgx 2 tg tgx 3 x k x k , k ( v担湛i tg 3 2)
- 3. Ba淡i 132 : (e thi tuye奪n sinh a誰i ho誰c kho叩i A, na棚m 2003) Gia短i ph旦担ng tr狸nh ( )2cos2x 1 cot gx 1 sin x sin2x * 1 tgx 2 = + + ieu kie辰n sin2x 0 va淡 tgx 1 Ta co湛 : ( )2 22 2 cos x cos x sin xcos2x cos x sin x sin x1 tgx cos x sin x1 cos x = = + ++ ( ) (= = +cos x cos x sin x do tgx 1 ne但n, sin x cos x 0) Do 単o湛 : ( ) ( )2 2cos x 1 * 1 cos x sin x cos x sin x sin 2x sin x 2 = + ( ) ( ) ( ) = = = = 2 cos x sin x 1 sin 2x sin x cos x sin x sin x cos x sin x cos x sin x 0 hay 1 sin x cos x sin x (**) ( ) ( ) = ｡ ｢ ｢ = ｢｣ 2 2 tgx 1 nha辰n so v担湛i tgx 1 1 sin x tg x do cos x 0 cos xcos x ( ) ( ) ｡ = + ｢ ｢ + =｢｣ = + 2 x k , k 4 2tg x tgx 1 0 vo但 nghie辰m x k , k nha辰n do sin 2x 0 4 L旦u y湛 : co湛 the奪 la淡m ca湛ch kha湛c ( ) ( ) 1 1 * * 1 sin 2x 1 cos2x 2 2 + =0 = + = + 3 sin 2x cos 2x 3 2 sin 2x : vo但 nghie辰m 4 Ba淡i 133 : Gia短i ph旦担ng tr狸nh ( )sin 3x cos3x 2cos x 0 *+ + = ( ) ( ) ( )3 3 * 3sin x 4sin x 4 cos x 3cos x 2cos x + + 0= =3 3 3sin x 4sin x 4cos x cos x 0 + V狸 cosx = 0 kho但ng la淡 nghie辰m ne但n chia hai ve叩 ph旦担ng tr狸nh cho ta 単旦担誰c 3 cos x 0 ( ) ( ) ( )2 3 2 * 3tgx 1 tg x 4tg x 4 1 tg x 0 + + + =
- 4. ( )( ) + + = =ｧ ｨ + =ｩ =ｧｪ ｨ + =ｪｩ = = 賊 = + = 賊 + 3 2 3 2 2 tg x tg x 3tgx 3 0 t tgx t t 3t 3 0 t tgx t 1 t 3 0 tgx 1 tgx 3 x k x k , k 4 3 Ba淡i 134 : Gia短i ph旦担ng tr狸nh ( )3 5sin4x.cos x 6sin x 2cos x * 2cos2x = ieu kie辰n : 2 2 cos2x 0 cos x sin x 0 tgx 1 賊 Ta co湛 : (*) 3 10sin 2x cos2x cos x 6sin x 2cos x 2cos2x cos2x 0 ｧ =ｪ ｨ ｪ ｩ 3 6sin x 2cos x 5sin 2x cos x tgx 1 ｧ = ｨ 賊ｩ ( )3 2 6sin x 2cos x 10sin x cos x * * tgx 1 ｧ =ｪ ｨ 賊ｪｩ Do cosx = 0 kho但ng la淡 nghie辰m cu短a (**), chia hai ve叩 ph旦担ng tr狸nh (**) cho ta 単旦担誰c3 cos x ( ) 2 6tgx 2 10tgx * * cos x tgx 1 ｧ =ｪ ｨ ｪ 賊ｩ ( )2 t tgx v担湛i t 1 6t 1 t 2 10t = ｧｪ ｨ + =ｪｩ 賊 = 賊 = 賊ｧ ｧ ｨ ｨ = + + =ｩ ｩ 3 2 t tgx v担湛i t 1 t tgx v担湛i t 1 3t 2t 1 0 (t 1) (3t 3t 1) 0 = 賊ｧ ｨ =ｩ t tgx v担湛i t 1 : vo但 nghie辰m t 1 Ba淡i 135 : Gia短i ph旦担ng tr狸nh ( )3 sin x 4 sin x cos x 0 * + = V狸 cosx = 0 kho但ng la淡 nghie辰m ne但n chia hai ve叩 ph旦担ng tr狸nh cho cos3 x th狸 ( ) ( )2 3 2 * tgx 1 tg x 4tg x 1 tg x + + + 0=
- 5. ( )( ) =ｧ ｨ + + + =ｩ =ｧｪ ｨ + +ｪｩ = = + 3 2 2 t tgx 3t t t 1 0 t tgx t 1 3t 2t 1 0 tgx 1 x k , k 4 = Ba淡i 136 : Gia短i ph旦担ng tr狸nh ( )( )2 2 tgx sin x 2sin x 3 cos2x sin x cos x * = + Chia hai ve叩 cu短a ph旦担ng tr狸nh (*) cho cos2 x ( ) ( )2 2 3 2 2 3 cos x sin x sin x cos x * tg x 2tg x cos x + = ( ) = +3 2 2 tg x 2tg x 3 1 tg x tgx ( )( ) + = =ｧ ｨ + =ｩ =ｧｪ ｨ + =ｪｩ = = 賊 = + = 賊 + 3 2 3 2 2 tg x tg x 3tgx 3 0 t tgx t t 3t 3 0 t tgx t 1 t 3 0 tgx 1 tgx 3 x k x k , k 4 3 Ba淡i 137 : Cho ph旦担ng tr狸nh ( ) ( ) ( ) ( ) ( )3 2 4 6m sin x 3 2m 1 sin x 2 m 2 sin x cos x 4m 3 cos x 0 * + + = a/ Gia短i ph旦担ng tr狸nh khi m = 2 b/ T狸m m 単e奪 ph旦担ng tr狸nh (*) co湛 duy nha叩t mo辰t nghie辰m tre但n 0, 4 ｡ ､ ｢ ･｣ ｦ Khi x 2 = + k th狸 cosx = 0 va淡 sin x 1= 賊 ne但n (*) tha淡nh : ( ) ( )4 6m 3 2m 1 0賊 賊 = 1 0 vo但 nghie辰m = chia hai ve (*) cho 3 cos x 0 th狸 ( ) ( ) ( ) ( ) ( ) ( )( )3 2 2 * 4 6m tg x 3 2m 1 tgx 1 tg x 2 m 2 tg x 4m 3 1 tg x 0 + + + + =2 )( ) ( ) (3 2 t tgx t 2m 1 t 3 2m 1 t 4m 3 0 * * =ｧｪ ｨ + + + =ｪｩ
- 6. ( )( )2 t tgx t 1 t 2mt 4m 3 0 =ｧｪ ｨ + =ｪｩ a/ Khi m = 2 th狸 (*) tha淡nh ( )( )2 t tgx t 1 t 4t 5 0 =ｧｪ ｨ + =ｪｩ = = + tgx 1 x k , k 4 b/ Ta co湛 : x 0, 4 ｡ ｢｣ ｦ ､ ･ th狸 [ ]tgx t 0,1= Xe湛t ph旦担ng tr狸nh : ( )2 t 2mt 4m 3 0 2 + = ( )2 t 3 2m t 2 = 2 t 3 2m t 2 = (do t = 2 kho但ng la淡 nghie辰m) a谷t ( ) ( ) 2 t 3 y f t C t 2 = = va淡 (d) y = 2m Ta co湛 : ( ) ( ) 2 2 t 4t y ' f t t 2 + = = 3 Do (**) luo但n co湛 nghie辰m t = 1 [ ]0,1 tre但n ye但u cau ba淡i toa湛n ( ) ( ) ( ) ( ) ｡ = ｢ =｢｣ d y 2m kho但ng co湛 単ie奪m chung v担湛i C d ca辿t C ta誰i1単ie奪m duy nha叩t t 1 3 2m 2m 2 2 < 3 m m 4 < 1 Ca湛ch kha湛c : Y C B T f(t) = ( )2 t 2mt 4m 3 0 2 + = vo但 nghie辰m tre但n [ .),0 1 Ta co湛 (2) co湛 nghie辰m [ ] ( ) , ( ). ( ) ( ) af f f hay af S モｧ ｪ モｪｪ ｨ ｪ ｪ ｪｩ 0 0 0 0 1 0 1 0 1 0 0 1 2
- 7. ( )( ) m m m m m hay m m ｧ + ｪ >ｪ ｨ >ｪ ｪ もｩ 2 4 3 0 4 3 0 4 3 2 2 0 2 2 0 0 1 m 3 1 4 Do 単o湛 (2) vo但 nghie辰m tre但n [ ), (m hay m hay f ) < > 3 0 1 1 1 0 4 = 3 m m 4 1 < BAI TAP 1. Gia短i ca湛c ph旦担ng tr狸nh sau : a/ 3 2 cos x sin x 3sin xcos x 0+ = b/ ( ) ( )2 sin x tgx 1 3sin x cos x sin x 3+ = + =c/ 2 2cos x cos2x sin x 0+ + d/ 3 2 3 1 cos x tg x 1 sin x = e/ 3 2 2 3 sin x 5sin xcos x 3sin xcos x 3cos x 0 + = f/ 3 2 cos x sin x 3sin xcos x 0+ = g/ 1 tgx 2 2 sin x+ = h/ 3 3 sin x cos x sin x cos x+ = k/ 2 2 3tg x 4tgx 4cot gx 3cot g x 2 0+ + + + = m/ ( sin ) cos ( ) cos x x tg x tgx x + + =2 2 2 3 1 3 8 4 2 0 n/ sin x cos x 1 sin 2x + = 2. Cho ph旦担ng tr狸nh : ( ) ( )2 2 sin x 2 m 1 sin x cos x m 1 cos x m+ + = a/ T狸m m 単e奪 ph旦担ng tr狸nh co湛 nghie辰m b/ Gia短i ph旦担ng tr狸nh khi m = -2 [ ]( )S : m 2,1 Th.S Ph畉m H畛ng Danh TT luy畛n thi 畉i h畛c CLC V挑nh Vi畛n