1. Hàm số $y=\dfrac{2\tan4x}{1-\tan^24x}$ là hàm tuần hoàn có chu kì $k\pi$ với hệ số $k$ bằng bao nhiêu?

2. Tập hợp nghiệm của phương trình $\tan(3x-15^o)=1$ trên khoảng $(-180^o;\,90^o)$ có số phần tử là bao nhiêu?

3. Với mọi giá trị của $x$, hàm số: $y=4(\sin^6x+\cos^6x)-5(\sin^4x+\cos^4x)-\dfrac{1}{4}\cos4x+\dfrac{1}{4}$ có giá trị không đổi là bao nhiêu?

4. Tính $A=\sin^4\dfrac{\pi}{16}+\sin^4\dfrac{3\pi}{16}+\sin^4\dfrac{5\pi}{16}+\sin^4\dfrac{7\pi}{16}$

5. Tìm max của $y=\dfrac{2\cos x+2}{\cos x+\sin x+2}$

4.
$A=\sin^4\dfrac{\pi}{16}+\sin^4\dfrac{3\pi}{16}+\sin^4\dfrac{5\pi}{16}+\sin^4\dfrac{7\pi}{16}$
$A=\sin^4\dfrac{\pi}{16}+\sin^4\dfrac{3\pi}{16}+\cos^4\left (\dfrac{\pi}{2}-\dfrac{5\pi}{16} \right )+\cos^4\left (\dfrac{\pi}{2}-\dfrac{7\pi}{16} \right )$
$A=\sin^4\dfrac{\pi}{16}+\sin^4\dfrac{3\pi}{16}+\cos^4\left (\dfrac{3\pi}{16} \right )+\cos^4\left (\dfrac{\pi}{16} \right )$
$A=\left ( \sin^2\dfrac{\pi}{16}+\cos^2\dfrac{\pi}{16} \right )^2-2\sin^2\dfrac{\pi}{16}.\cos^2\dfrac{\pi}{16}+\left ( \sin^2\dfrac{3\pi}{16}+\cos^2\dfrac{3\pi}{16} \right )^2-2\sin^2\dfrac{3\pi}{16}.\cos^2\dfrac{3\pi}{16}$
$A=1-\dfrac{1}{2}\sin^2\dfrac{\pi}{8}+1-\dfrac{1}{2}\sin^2\dfrac{3\pi}{8}$
$A=2-\dfrac{1}{2}\sin^2\dfrac{\pi}{8}-\dfrac{1}{2}\cos^2\left (\dfrac{\pi}{2}-\dfrac{3\pi}{8} \right )$
$A=2-\dfrac{1}{2}\sin^2\dfrac{\pi}{8}-\dfrac{1}{2}\cos^2\dfrac{\pi}{8}$
$A=2-\dfrac{1}{2}=\dfrac{3}{2}$






5.
$y=\dfrac{2\cos x+2}{\cos x+\sin x+2}\Leftrightarrow y\cos x+y\sin x+2y=2\cos x+2$
$\Leftrightarrow (y-2)\cos x+y\sin x=2-2y$
Để PT có nghiệm thì ta phải có $(2-2y)^2 \le (y-2)^2+y^2 \Leftrightarrow (2-2y)^2- (y-2)^2-y^2 \le 0$
$y(y-2) \le 0\Leftrightarrow 0 \le y \le 2.$
Vậy $\max y =2\Leftrightarrow (2-2)\cos x+2\sin x=2-2.2\Leftrightarrow \sin x =-1.$
3.
$y=4(\sin^6x+\cos^6x)-5(\sin^4x+\cos^4x)-\dfrac{1}{4}\cos4x+\dfrac{1}{4}$
$y=4\left[ {(\sin^2x+\cos^2x)^3-3\sin^2x.\cos^2x(\sin^2x+\cos^2x)} \right]-5\left[ {(\sin^2x+\cos^2x)^2-2\sin^2x.\cos^2x} \right]-\dfrac{1}{4}\cos4x+\dfrac{1}{4}$
 $y=4\left[ {1-3\sin^2x.\cos^2x} \right]-5\left[ {1-2\sin^2x.\cos^2x} \right]-\dfrac{1}{4}\left ( 1-2\sin^22x \right )+\dfrac{1}{4}$
  $y=4-12\sin^2x.\cos^2x-5+10\sin^2x.\cos^2x-\dfrac{1}{4}+2\sin^2x.\cos^2x +\dfrac{1}{4}$
 $y=-1$
2.
$\tan(3x-15^o)=1=\tan 45^o\Leftrightarrow 3x-15^o=45^o + k180^o \Leftrightarrow 3x=60^o + k180^o\quad k \in \mathbb Z.$
Ta có
$\Leftrightarrow \begin{cases}-180^o<x<90^o \\ k \in \mathbb Z \end{cases} \Leftrightarrow \begin{cases}-540^o<3x<270^o \\ k \in \mathbb Z \end{cases}$
$\Leftrightarrow \begin{cases}-540^o<60^o + k180^o<270^o \\ k \in \mathbb Z \end{cases}\Leftrightarrow \begin{cases}-600^o<  k180^o<210^o \\ k \in \mathbb Z \end{cases}$
$\Leftrightarrow \begin{cases}-3\le  k\le 1 \\ k \in \mathbb Z \end{cases}\Rightarrow k \in \left\{ {-3,-2,-1,0,1} \right\}$
 Như vậy PT trên có $5$ nghiệm.
1.
$y=\dfrac{2\tan4x}{1-\tan^24x}=\dfrac{2\dfrac{\sin 4x}{\cos4x}}{1-\dfrac{\sin^2 4x}{\cos^24x}}=\dfrac{2\dfrac{\sin 4x}{\cos4x}}{\dfrac{\cos^24x-\sin^2 4x}{\cos^24x}}=\dfrac{2\dfrac{\sin 4x}{\cos4x}}{\dfrac{\cos8x}{\cos^24x}}=2\dfrac{\sin 4x\cos 4x}{\cos8x}=\tan 8x$
Như vậy $y=f(x)=\tan 8x$
Nên  $f(x+\dfrac{\pi}{8})=\tan (8x+8.\dfrac{\pi}{8})=\tan (8x+\pi)=\tan 8x =f(x)$
Như vậy $k=\dfrac{1}{8}$.

Bạn cần đăng nhập để có thể gửi đáp án

Chat chit và chém gió
  • hoahoa.nhynhay: . 11/5/2018 1:39:46 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:46 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:46 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:46 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:47 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:47 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:47 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:47 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:49 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:49 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:49 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:49 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:50 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:50 PM
  • hoahoa.nhynhay: ..................... 11/5/2018 1:39:52 PM
  • vinhlyle: hi 11/10/2018 8:03:02 PM
  • ๖ۣۜBossღ: 3:00 AM 11/11/2018 10:17:11 PM
  • quanghungnguyen256: sao wweb cứ đăng nhập mãi nhĩ, k trả lời đc bài viết nữa 11/30/2018 4:35:45 PM
  • quanghungnguyen256: web nát r à 11/30/2018 4:36:19 PM
  • quanghungnguyen256: 11/11/2018 h là 30/11. oi web chắt k ai dùng r hả 11/30/2018 4:36:44 PM
  • quanghungnguyen256: rofum ngon thế mà sao admin lại k nâng cấp nhỡ 11/30/2018 4:37:07 PM
  • nguyenlena2611: talk_to_the_hand 12/24/2018 9:24:22 PM
  • nguyenlena2611: big_grinsurpriseblushing 12/24/2018 9:28:35 PM
  • Việt EL: ^^ 2/16/2019 8:37:21 PM
  • Việt EL: he lô he lô 2/16/2019 8:37:34 PM
  • Việt EL: y sờ e ny guan hiar? 2/16/2019 8:38:15 PM
  • Việt EL: èo 2/16/2019 8:38:32 PM
  • Việt EL: éo có ai 2/16/2019 8:40:48 PM
  • dfgsgsd: Hế lô 2/21/2019 9:52:51 PM
  • dfgsgsd: Lờ ôn lôn huyền ..... 2/21/2019 9:53:01 PM
  • dfgsgsd: Cờ ắc cắc nặng.... 2/21/2019 9:53:08 PM
  • dfgsgsd: Chờ im.... 2/21/2019 9:53:12 PM
  • dfgsgsd: Dờ ai dai sắc ...... 2/21/2019 9:53:23 PM
  • dfgsgsd: ờ ưng nưng sắc.... 2/21/2019 9:53:37 PM
  • dfgsgsd: Mờ inh minh huyền.... đờ ep nặng... trờ ai... quờ a sắc.... đờ i.... 2/21/2019 9:54:11 PM
  • nln: winking 2/28/2019 9:02:14 PM
  • nln: big_grin 2/28/2019 9:02:16 PM
  • nln: smug 2/28/2019 9:02:18 PM
  • nln: talk_to_the_hand 2/28/2019 9:02:20 PM
  • nln: Specialise 2/28/2019 9:51:54 PM
  • nlnl: But they have since become two much-love 2/28/2019 10:03:10 PM
  • dhfh: sad 3/2/2019 9:27:26 PM
  • ๖ۣۜNatsu: allo 3/3/2019 11:39:32 PM
  • ffhfdh: reyeye 3/5/2019 8:53:26 PM
  • ffhfdh: ủuutrr 3/5/2019 8:53:29 PM
  • dgdsgds: ujghjj 3/24/2019 9:12:47 PM
  • ryyty: ghfghgfhfhgfghgfhgffggfhhghfgh 4/9/2019 9:34:48 PM
  • gdfgfd: gfjfjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj 4/14/2019 9:53:38 PM
  • gdfgfd: sadsadsadsadsadsad 4/14/2019 9:59:30 PM
  • fdfddgf: trâm anh 4/17/2019 9:40:50 PM
  • gfjggg: a lot of advice is available for college leavers 5/10/2019 9:32:12 PM
  • linhkim2401: big_hug 7/3/2019 9:35:43 AM
  • ddfhfhdff: could you help me do this job 7/23/2019 10:29:49 PM
  • ddfhfhdff: i don't know how to 7/23/2019 10:30:03 PM
  • ddfhfhdff: Why you are in my life, why 7/23/2019 10:30:21 PM
  • ddfhfhdff: Could you help me do this job? I don't know how to get it start 7/23/2019 10:31:45 PM
  • ddfhfhdff: big_grinwhistling 7/23/2019 10:32:50 PM
  • ddfhfhdff: coukd you help me do this job 7/23/2019 10:39:22 PM
  • ddfhfhdff: i don't know how to get it start 7/23/2019 10:39:38 PM
  • huy31012002:9/13/2019 10:43:52 PM
  • huongpha226: hello 11/29/2019 8:22:41 PM
  • hoangthiennhat29: pig 4/2/2020 9:48:11 PM
  • cutein111: . 4/9/2020 9:23:18 PM
  • cutein111: . 4/9/2020 9:23:19 PM
  • cutein111: . 4/9/2020 9:23:20 PM
  • cutein111: . 4/9/2020 9:23:22 PM
  • cutein111: . 4/9/2020 9:23:23 PM
  • cutein111: hello 4/9/2020 9:23:30 PM
  • cutein111: mấy bạn 4/9/2020 9:23:33 PM
  • cutein111: mấy bạn cần người ... k 4/9/2020 9:23:49 PM
  • cutein111: mik sẽ là... của bạn 4/9/2020 9:23:58 PM
  • cutein111: hihi 4/9/2020 9:24:00 PM
  • cutein111: https://www.youtube.com/watch?v=EgBJmlPo8Xw 4/9/2020 9:24:12 PM
  • nhdanfr: Hello 9/17/2020 8:34:26 PM
  • minhthientran594: hi 11/1/2020 10:32:29 AM
  • giocon123fa: hi mọi ngừi :33 1/31/2021 10:31:56 PM
  • giocon123fa: call_me 1/31/2021 10:32:46 PM
  • giocon123fa: không còn ai nữa à? 1/31/2021 10:36:35 PM
  • giocon123fa: toi phải up cái này lên face để mọi người vào chơilaughing) 1/31/2021 10:42:37 PM
  • manhleduc712: hí ae 2/23/2021 8:51:42 AM
  • vaaa: f 3/27/2021 9:40:49 AM
  • vaaa: fuck 3/27/2021 9:40:57 AM
  • L.lawiet: l 6/4/2021 1:26:16 PM
  • tramvin1: . 6/14/2021 8:48:20 PM
  • dothitam04061986: solo ff ko 7/7/2021 2:47:36 PM
  • dothitam04061986: ai muốn xem ngực e ko ạ 7/7/2021 2:49:36 PM
  • dothitam04061986: e nứng 7/7/2021 2:49:52 PM
  • Phương ^.^: ngủ hết rồi ạ? 7/20/2021 10:16:31 PM
  • ducanh170208: hi 8/15/2021 10:23:19 AM
  • ducanh170208: xin chao mọi người 8/15/2021 10:23:39 AM
  • nguyenkieutrinh: hiu lo m.n 9/14/2021 7:30:55 PM
  • nguyenngocha651: Xin chào tất cả các bạn 9/20/2021 3:13:46 PM
  • nguyenngocha651: Có ai onl ko, Ib với mik 9/20/2021 3:14:08 PM
  • nguyenngocha651: Còn ai on ko ạ 9/20/2021 3:21:34 PM
  • nguyenngocha651: ai 12 tủi, sinh k9 Ib Iw mik nhố 9/21/2021 10:22:38 AM
Đăng nhập để chém gió cùng mọi người
  • dvthuat
  • hoàng anh thọ
  • nhungtt0312
  • Xusint
  • tiendat.tran.79
  • babylove_yourfriend_1996
  • thaonguyenxanh1369
  • hoangthao0794
  • zzzz1410
  • watashitipho
  • HọcTạiNhà
  • Cá Hêu
  • peonycherry
  • phanqk1996
  • giothienxung
  • khoaita567
  • nguyentranthuylinhkt
  • maimatmet
  • minh.mai.td
  • quybalamcam
  • m_internet001
  • bangtuyettrangsocola
  • chizjzj
  • vuivequa052
  • haibanh237
  • sweetmilk1412
  • panhhuu
  • mekebinh
  • Nghịch Thuỷ Hàn
  • Lone star
  • LanguaeofLegend
  • huongduong2603
  • i_love_you_12387
  • a ku
  • heohong_congchua
  • impossitable111
  • khanh
  • ๖ۣۜJinღ๖ۣۜKaido
  • huynhhoangphu.10k7
  • namduong2016
  • vycreepers
  • Bảo Phươngg
  • Yurika Yuki
  • tinysweets98
  • Thùy Trang
  • Hàn Thiên Dii
  • ๖ۣۜConan♥doyleღ
  • LeQuynh
  • thithuan27
  • huhunhh
  • ๖ۣۜDemonღ
  • nguyenxinh6295
  • phuc642003
  • diephuynh2009
  • Lê Giang
  • Han Yoon Min
  • ...
  • thuyvan
  • Mặt Trời Bé
  • DoTri69
  • bac1024578
  • Hạ Vân
  • thuong0122
  • nhakhoahoc43
  • tuanngo.apd
  • Đức Vỹ
  • ๖ۣۜCold
  • Lethu031193
  • salihova.eldara