y=sin2xcos2x怎么化简 函数y=sin2xcos2x怎么化简

y=sin2x-cos2x\u600e\u4e48\u5316\u7b80

y
=sin2x-cos2x
=\u221a2.sin(2x-\u03c0/4)

(1/2)*sin4x
\u89e3\uff1a
y
=sin2xcos2x
=(1/2)*2sin2xcos2x
=(1/2)*sin4x
PS\uff1a\u4ea6\u53ef\u4ee5\u5316\u4e3a\u5176\u5b83\u5f62\u5f0f

根据2倍角公式sin(2x)=2sinxcosx，得
y=sin2xcos2x=1/2(2sin2xcos2x)=1/2sin4x

y=sin2xcos2x
=1/2*2*sin2xcos2x
=1/2sin4x(半角公式)

用二倍角公式
y=1/2sin4x

用倍用公式
y=sin2xcos2x=1/2sin4x

你是要化简成什么样的啊
y=sin2xcos2x=1/2sin4x，这个可以不？

y=sin2xcos2x鎬庝箞鍖栫畝?
绛旓細y=sin(2x)cos(2x)=(1/2)sin(4x)

y=sin²x.cos2x鎬庝箞鍖栬В?
绛旓細y=sin^2(x)cos2x=(1-cos2x)/2*cos2x=(cos2x)/2-(cos2x)^2/2=(cos2x)/2-(1 cos4x)/4 y'= -sin2x sin4x

y=sin2xcos2x鎬庝箞鍖栫畝
绛旓細鏍规嵁2鍊嶈鍏紡sin(2x)=2sinxcosx锛屽緱 y=sin2xcos2x=1/2(2sin2xcos2x)=1/2sin4x

鍑芥暟y=sin2xcos2x鎬庝箞鍖栫畝
绛旓細瑙ｏ細y =sin2xcos2x =(1/2)*2sin2xcos2x =(1/2)*sin4x PS锛氫害鍙互鍖栦负鍏跺畠褰㈠紡

y=sin2xcos2x鍖栫畝鎬庝箞鍒皔=sin4x/2鐨,瑕佸叿浣撴楠
绛旓細涓夎鍑芥暟鍏紡sin2t=2sintcost (sin2t)/2=sintcost 浠2x=t y=sin2xcos2x=sintcost=(sin2t)/2 2t=4x 鎵浠 y=sin2xcos2x=锛坰in4x锛/2

y=sin2xcos2x鍖栫畝鎬庝箞鍒皔=sin4x/2鐨,
绛旓細涓夎鍑芥暟鍏紡sin2t=2sintcost (sin2t)/2=sintcost 浠2x=t y=sin2xcos2x=sintcost=(sin2t)/2 2t=4x 鎵浠 y=sin2xcos2x=锛坰in4x锛/2

y=sin2xcos2x鎬庝箞鍖栨垚鏈绠鍗曠殑寮忓瓙?
绛旓細绛旀锛歽=1/2sin4x 鍛愶紝涓轰簡鏂逛究锛屾垜浠笉濡ㄤ护2x=A 閭ｄ箞y=sinAcosA =1/2*2sinAcosA =1/2sin2A(涓よ灏嗗叕寮忥級=1/2sin4x 鍘勶紝鎳傚惁锛熸ゼ涓婂ソ鍍忛敊浜嗐

鍑芥暟y=sin2xcos2x鎬庝箞鍖栨垚1/2 sin4x,姹傝繃绋
绛旓細鏍规嵁2鍊嶈鍏紡锛歴in(2x)=2sinxcosx y=sin2xcos2x=1/2(2sin2xcos2x)=1/2sin4x

y=sin2xcos2x=1/2sin4x鎬庝箞鍋氱殑姹傝缁嗚繃绋
绛旓細瑙ｏ細宸茬煡锛y=sin2xcos2x 鍙樻崲锛歽=(1/2)(2sin2xcos2x)鐢卞嶈鍏紡锛歽=(1/2)sin(4x)

鍑芥暟y=sin2x鎬庢牱杞崲涓簓=cos2x
绛旓細y=cos2x=sin锛埾/2-2x锛=-sin(2x-蟺/2)搴旀妸鈶y=sin2x鍚戝彸骞崇Щ蟺/4涓崟浣 鈶℃í鍧愭爣涓嶅彉,绾靛潗鏍囧彉涓哄師鏉ョ殑-1鍊