cos2x-sin2x怎么化简 cos4x-sin2x怎么化简成sin
sin2x+cos2x\u600e\u4e48\u5316\u7b80sin2x+cos2x
= \u221a2\u00b7\u3010cos45\u00b7sin2X + sin45\u00b7cos2X\u3011
= \u221a2\u00b7sin[2X + 45]
\u5bf9\u5427 \u52a0\u6cb9
\u8fd9\u4e2a\u5c31\u662f\u7528 sin2x=2sinxcosx\u7684\u516c\u5f0f\u554a\uff0c\u4f60\u8981\u662f\u770b\u4e0d\u61c2\u5c31\u7528a=2x\uff0c\u90a3\u4e48\u539f\u5f0f\u5c31\u662fy=sinacosa=1/2sin2a\u4e86\uff0c\u8fd9\u4e2a\u771f\u7684\u8be6\u7ec6\u4e0d\u8d77\u6765\u4e86
cos2x-sin2x=√2*(cos2x*√2/2 - sin2x*√2/2)
=√2*[cos2x*cos(π/4) - sin2x*sin(π/4)]
=√2*cos(2x+ π/4)
绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀
绛旓細cos2x*sin2x =1/2*2*sin2xcos2x =1/2*sin4x
绛旓細sin2X=2sinXcosX cos2X=cosX^2-sinX^2 cosX^2+sinX^2=1 浠ｅ叆鍏紡鏈 鍘熷紡=2sinXcosX-锛坈osX^2-sinX^2锛=cosX^2+sinX^2=1 鎵浠ユ湁2sinXcosX=2cosX^2 鎵浠ユ湁cosX鎴栦笉绛変簬0涓ょ鎯呭喌 褰揷osX=0鏃讹紝 sinX=1鎴-1 姝ゆ椂X绛変簬 2k蟺+蟺/2 鎴(2k+1)蟺+蟺/2 褰揷osX涓嶇瓑浜0鏃 co...
绛旓細f(x)=sin2x-cos2x =鈭2*[sin2x*(鈭2)/2 - cos2x*(鈭2)/2]=鈭2*[sin2x*cos(蟺/4) -cos2x*sin(蟺/4)]=鈭2*sin(2x-蟺/4)
绛旓細2cos2x+sin^2x =2(cos^2x-sin^2x)+sin^2x =2cos^2x-sin^2x =3cos^2x-1
绛旓細f(x)=cos2x+sin2x=鈭2*(鈭2/2*cos2x+鈭2/2*sin2x)=鈭2sin(2x+蟺/4) 鎵浠(x)鐨勬渶灏忔鍛ㄦ湡=2蟺/2=蟺 濡傛灉鍑芥暟g(x)=sin(mx+n)+C (m,n鍜孋鍧囦负甯告暟) 閭ｄ箞鍑芥暟鏈灏忔鍛ㄦ湡=2蟺/m 寰堥珮鍏翠负鎮ㄨВ绛旓紝绁濆涔犺繘姝ワ紒 鏈変笉鏄庣櫧鐨勫彲浠ヨ拷闂紒 濡傛灉鎮ㄨ鍙垜鐨勫洖绛旓紝璇风偣鍑讳笅闈㈢殑...
绛旓細鎴戜滑鍙互鍒╃敤涓夎鍑芥暟鐨勫嶈鍏紡鏉ュ $\sin 2x + \cos 2x$ 杩涜鍖栫畝銆傚叿浣撹繃绋嬪涓嬶細\begin{aligned} \sin 2x + \cos 2x &= 2\sin x \cos x + (\cos^2 x - \sin^2 x) &&\text{(鍒╃敤涓夎鍑芥暟鐨勫嶈鍏紡)} \ &= 2\sin x \cos x + \cos^2 x - \sin^2 x &&\text{(...
绛旓細鍖栫畝棰 cos^2xsin^2x涓轰粈涔堢瓑浜1/8(1-cos4t) 鎴戞潵绛 2涓洖绛 #鐑# 浣滀负濂虫,浣犵敓娲讳腑鏈夋劅鍙楀埌鈥滀笉瀹夊叏鎰熲濈殑鏃跺埢鍚?甯呭竻涓鐐伆 2015-06-10 路 鐭ラ亾鍚堜紮浜烘暀鑲茶瀹 甯呭竻涓鐐伆 鐭ラ亾鍚堜紮浜烘暀鑲茶瀹 閲囩撼鏁:6862 鑾疯禐鏁:60030 鍚慣A鎻愰棶 绉佷俊TA 鍏虫敞 灞曞紑鍏ㄩ儴 杩界瓟 绛旈涓嶆槗,濂借瘎鍝 ...
绛旓細鏍规嵁2鍊嶈鍏紡sin(2x)=2sinxcosx锛屽緱 y=sin2xcos2x=1/2(2sin2xcos2x)=1/2sin4x
绛旓細sin^2x宸茬粡鏄渶绠鐨勪簡涓嶉渶瑕鍖栫畝銆傚鏋sin2x涓殑2涓嶆槸骞虫柟鑰屾槸鎸2x锛屽垯鍙牴鎹叕寮忓緱sin2x=2sinx•cosx銆1+cos2x锛氬叾涓璫os2x=2cos²x-1锛屾墍浠1+cos2x=1+2cos²x-1=2cos²x銆
