1-2sinxcosx 高一下学期的数学:1).证明1-2sinxcosx/cos&...

\u4e3a\u4ec0\u4e481-2cosx>0

\u770b\u4f60\u4e5f\u6c42\u5bfc\u7b97\u4e86\uff0c\u77e5\u9053x=\u03a0/3\uff0860\u00b0\uff09\u4e3a\u6781\u5c0f\u503c\u70b9\u3002
\u4e3a\u4ec0\u4e481-2cosx>0\uff0c\u4f60\u8fd9\u95ee\u6cd5\u4e0d\u5bf9\uff0c\u8fd9\u4e2a\u6c42\u7684\u5c31\u662fx\u7b26\u5408\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\u7684\u53d6\u503c\u8303\u56f4\u3002
\u8fd8\u6709 \u6c42\u5bfc\u5c31\u662f\u6c42\u51fd\u6570\u7684\u589e\u51cf\u8d8b\u52bf\u3002
\u5c31\u8fd9\u4e2a\u9898\u6765\u8bf4
1-2cosx>0\uff0c\u6c42\u51fa\u7684x\u8303\u56f4\uff0c\u5c31\u662f\u8be5\u51fd\u6570\u7684\u589e\u533a\u95f4\u3002
1-2cosx<0\uff0c\u6c42\u51fa\u7684x\u8303\u56f4\uff0c\u5c31\u662f\u8be5\u51fd\u6570\u7684\u51cf\u533a\u95f4\u3002
1-2cosx=0\uff0c\u6c42\u51fa\u7684x\u7684\u503c\uff0c\u5c31\u662f\u8be5\u51fd\u6570\u7684\u6781\u503c
1-2cosx=0\uff0c\u6c42\u51fax=\u03a0/3\uff0860\u00b0\uff09\u3002\u8fdb\u800c\u53ef\u4ee5\u5f97\u51fa\uff0c\u51fd\u6570\u5728\u03a0/3\u5468\u56f4\uff0c\u5de6\u9012\u51cf\u53f3\u9012\u589e\uff0c\u81ea\u7136\u03a0/3\u4e3a\u8be5\u51fd\u6570\u7684\u6781\u5c0f\u503c\u70b9\uff0c\u5e26\u5165\u539f\u5f0f\u7684\u6781\u5c0f\u503c\u4e3a \u6839\u53f7\u4e09\u3002

\u9898\u76ee\u7b26\u53f7\u4e0d\u6e05\u695a\uff0c\u6240\u4ee5\u7b54\u6848\u53ef\u80fd\u6709\u5f88\u591a\u79cd\u3002
\u5176\u4e2d\u4e00\u79cd\u662f\uff1a
sinx\u00f7|sinx|+|cosx|\u00f7cosx+tanx\u00f7|tanx\u7684\u503c\u57df
|\u2235sinx\u22600\uff0ccosx\u22600\uff0ctanx\u22600
\u2234x\u2260k\u220f/2\uff0ck\u2208z\uff0c
\u5373x\u7684\u7ec8\u8fb9\u4e0d\u5728\u5750\u6807\u8f74\u4e0a\u3002
\u53ef\u4ee5\u5206\u56db\u4e2a\u8c61\u9650\u8ba8\u8bba\uff1a
x\u662f\u7b2c\u4e00\u8c61\u9650\u89d2\uff0csinx>0,cosx>0,tanx>0\uff0cy=3
x\u662f\u7b2c\u4e8c\u8c61\u9650\u89d2\uff0csinx>0,cosx<0,tanx<0\uff0cy=\uff0d1
x\u662f\u7b2c\u4e09\u8c61\u9650\u89d2\uff0csinx0\uff0cy=\uff0d1
x\u662f\u7b2c\u56db\u8c61\u9650\u89d2\uff0csinx0,tanx<0\uff0cy=\uff0d1
\u2234\u503c\u57df\u4e3a{3\uff0c\uff0d1}
\u4e5f\u5c31\u662f\u53ea\u6709\u4e24\u4e2a\u503c
\uff0c3\uff0c-1
\uff0c\u503c\u57df\u4e3a
\uff5b3\uff0c-1\uff5d

∵sin²x+cos²x=1

∴1-2sinxcosx
=sin²x+cos²x-2sinxcosx
=(sinx-cosx)²

有一个恒等式
sin²x+cos²x=1

1-2sinxcosx
绛旓細鈭1-2sinxcosx =sin²x+cos²x-2sinxcosx =(sinx-cosx)²

1-2sinxcosx绛変簬澶氬皯
绛旓細1-sin2x

宸茬煡sinx路cosx=1/6,涓斚/4<x<蟺/2,鍒檆osx-sinx鐨勫肩瓑浜?
绛旓細-鈭6/3 鏍规嵁鍏紡锛(cosx-sinx)²=1-2sinxcosx=1-1/3=2/3 鎵浠 cosx-sinx=+-鈭6/3 鍥犱负 蟺/4<x<蟺/2,鎵浠 蟺/2<x+蟺/4<3蟺/4,鎵浠 cosx-sinx<0 鎵浠 cosx-sinx=-鈭6/3 琛ュ厖涓浜涗笁瑙掑嚱鏁板叕寮忥細鍊嶈鍏紡 Sin2A=2SinA?CosA Cos2A=CosA^2-SinA^2=1-2S...

姹傝瘉:(1)1-2sinxcosx鍒嗕箣cos骞虫柟x-sin骞虫柟x=1-tanx鍒嗕箣1+tanx
绛旓細cos骞虫柟x-sin骞虫柟x=锛坈osx-sinx锛夛紙cosx+sinx锛1-2sinxcosx=cos骞虫柟x+sin骞虫柟x-2sinxcosx=锛坈osx-sinx锛夊钩鏂瑰墠涓ゅ紡鍙互绾︽帀涓涓猚osx-sinx锛屽緱鍒扮殑寮忓瓙涓よ竟涓婁笅鍐嶅悓鏃堕櫎浠osx锛屽氨寰楀埌鍙宠竟鐨勫紡瀛愪簡銆

鍑芥暟y=鈥1鈥2sinxcosx鐨勬渶灏忓兼槸
绛旓細y=2(1/2+sinx)/(a+cosx) 涓婂紡鐨勭墿鐞嗘剰涔夋槸鐐(1/2,a)涓庡崟浣嶅渾涓婄殑鐐硅繛绾跨殑鏂滅巼鐨2鍊嶃

cosx(1-2sinx)姹傚,鍏蜂綋杩囩▼
绛旓細灞曞紑鐨勮瘽锛屼細鏇村ソ銆傚睍寮鍚庝负锛歝osx-2sinxcosx = cosx-sin(2x);姹傚涓猴細-sin x - 2cos(2x)

cosx/(1-2sinx) 鍊煎煙 瑕佸垵绛夋帹瀵艰繃绋,瀵兼暟浠涔堢殑閫鏁
绛旓細浠=cosx/(1-2sinx)锛屽垯 t-2tsinx=cosx 鎵浠 2tsinx+cosx=t 鈭(4t^2+1)sin(x+a)=t (鍏朵腑 tana=1/(2t))鎵浠 鈭(4t^2+1)鈮t|锛屽钩鏂瑰緱 4t^2+1鈮^2 瑙ｅ緱 t鈭圧锛堝叏浣撳疄鏁帮級

姹倅=1-2sinx+cosx鐨勫煎煙
绛旓細瑙ｏ細y=1-鈭5sin(x+Q)鎵浠ュ煎煙[1-鈭5,1+鈭5]鈭5涓烘牴鍙蜂笅5

涓嶅畾绉垎cosx-sinx/1-2cosxsinx?
绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀

鏍瑰彿涓1-sin2x鐨勫畾绉垎 0鍒颁簩鍒嗕箣娲 姹傝В
绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀

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