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Nội dung: <blockquote data-quote="gaconti14" data-source="post: 9983" data-attributes="member: 12660">Công thức ? ý bạn là công thức gì bài đó rõ lắm rồi còn gì ?Còn nếu hỏi công thức lượng giác thì đâyCác hàm lượng giác:<img src="https://upload.wikimedia.org/math/2/c/3/2c364ad9484a8aa98d84cd066c015032.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/f/7/5/f7555a262cbf5a97a810d4ca9ec676d2.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Tuần hoàn: <img src="https://upload.wikimedia.org/math/a/d/e/ade60bebb32ce18853dde18bea8788c2.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> <img src="https://upload.wikimedia.org/math/c/4/b/c4b61d5490af84f1b096b5a647f4b132.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/8/1/7/8179dd0a71db0793f02c4d481486d467.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Đối xứng:<img src="https://upload.wikimedia.org/math/e/2/3/e23fa842b23102e20a11a61a7a1b962e.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/5/0/1/5012904c75a6f2c44aaf1d0308f63fda.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/1/2/7/127650e424ff1c0a55750cfa81a70e61.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/d/9/2/d92ac069c6b11dcc6328f638c1c5a613.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Tịnh  tiến:<img src="https://upload.wikimedia.org/math/1/1/6/116ebb88d0e49cde0ab76ae24a129788.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/5/c/b/5cb1fa1fd052dabe72d3be25882891d4.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/e/f/9/ef99de492a256c296e25d554b06d4928.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Đẳng thức sau cũng đôi khi hữu ích:<img src="https://upload.wikimedia.org/math/b/2/3/b23b076defb7225db5ddd5682263d88c.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />với <img src="https://upload.wikimedia.org/math/3/4/1/3419edec72040aa60e2f4a06e21b6ff7.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Đẳng thức Pytago<img src="https://upload.wikimedia.org/math/2/1/0/21010ba21c3a658c1bebe44ec023322e.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/8/0/b/80b2e731371b16456f9896a3acc6486a.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/3/7/2/3720f8d94ba670f815511b964e8ca39b.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Tổng của hiệu và góc:<img src="https://upload.wikimedia.org/math/9/6/1/96188065d4eefcdb83c5b7365f96eaa4.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/6/6/4/664f8e8310a75a6d41e5e856d9e68c2d.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/8/1/c/81cacd83df440beb2ec3c30095e93308.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Công thức góc bộiBội hai<img src="https://upload.wikimedia.org/math/f/e/6/fe6cc975b1dfa6a6eb138084efbbc27c.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/d/4/7/d47d2157e706c5f9babc8395f47f0553.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/7/f/6/7f643709c0d69e839822f3749fc95083.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Bội ba sin(3x) = 3sin(x) − 4sin3(x) cos(3x) = 4cos3(x) − 3cos(x) Công thức hạ bậc<img src="https://upload.wikimedia.org/math/8/b/b/8bbde03904651d44e07ab31fcab6f347.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/9/0/7/907b46531052621b3506c52611b08040.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/b/1/f/b1f41f40bc24aadf72d79111a9dd67e1.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/4/c/2/4c2c449379255a8b71c354c3f857d7e1.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/4/8/4/484d6cae87865dad7b188fb25b10bd76.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/3/7/b/37b0ba6be2c6e6a85e34f3b31a854885.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Công thức góc chia đôi:Thay x/2 cho x trong công thức trên, rồi giải phương trình cho cos(x/2)  và sin(x/2) để thu được:<img src="https://upload.wikimedia.org/math/6/f/b/6fb0bcb5dae69c63766b1bcbc287d643.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/c/d/4/cd425bbc22429e4c520b81abe6cb4c6e.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Dẫn đến:<img src="https://upload.wikimedia.org/math/8/c/9/8c9b1adbd2afab0ffb4cdc1c475326f0.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Nhân với mẫu số và tử số 1 + cos x, rồi dùng định lý Pytago để đơn giản  hóa:<img src="https://upload.wikimedia.org/math/2/9/8/2982e078e21bc8ad1afb19480a1e7485.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/2/8/1/28162ee4817001cc3f4045cf90cee949.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Tương tự, lại nhân với mẫu số và tử số của phương trình (1) bởi 1 − cos  x, rồi đơn giản hóa:<img src="https://upload.wikimedia.org/math/4/6/2/462c5f8b96c299629047cc6e59b83faa.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/a/c/7/ac77560f4f55a15eaa139b5bb60037da.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Suy ra:<img src="https://upload.wikimedia.org/math/7/f/b/7fb090113e3c99b6c4cbd80972979255.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Nếu:<img src="https://upload.wikimedia.org/math/6/3/6/63688bbdcf691370a622c90fa5ff9483.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />thì:<img src="https://upload.wikimedia.org/math/b/2/a/b2a63ea30b3ba68ea07b4b1076c1639d.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://upload.wikimedia.org/math/c/7/c/c7c46de9e797429e996c5f44949d5d46.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Biến tích thành tổng:<img src="https://upload.wikimedia.org/math/0/0/7/007edc9607631d730f9b30132e99a1b7.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/8/8/1/8818ace904626998a66cadf0f0a7396f.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/c/3/2/c3254b31d1adba7d7b5d8c7a2fad54df.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/6/6/3/6637338e03dd995084fe65e41e5109f2.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Biển tổng thành tích:Thay x bằng (x + y) / 2 và y bằng (x – y) / 2 trong công thức trên, suy  ra:<img src="https://upload.wikimedia.org/math/f/1/f/f1febb04037fe1c4436c42aa379455f1.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/d/5/1/d51e35bc031c4ed60bff6b3f2d786075.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/4/3/0/430e4d24e25784069ab245a32a7f9561.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://upload.wikimedia.org/math/a/5/b/a5bb9a21fe6ccf7e3c4a3e2ac61ebea2.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Chú ý cos x + sin x=Căn 2 của Sin(x+pi/4)=Căn 2 của Cos(x-pi/4)cos x - sin x=Căn 2 của Sin(x-pi/4)=Căn 2 của Cos(x+pi/4)1 số bài tập còn ứng dụng việc đặt tan (x/2)=t nữa*Tan (x/2)=t :Sin x=2t/(t^2+1)Cos x=(1-t^2)/(1+t^2)Tan x= 2t/(1-t^2)dt=(1+t^2)/2 dx (Cái này lớp 12 ) <img src="https://cdn.jsdelivr.net/gh/twitter/twemoji@14.0.2/assets/72x72/1f600.png" class="smilie smilie--emoji" loading="lazy" width="72" height="72" alt=":D" title="Big grin    :D"  data-smilie="8"data-shortname=":D" /></blockquote>

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