sin2X-cos2X可以被化简成什么 y=sin2x-cos2x怎么化简

sin2X-cos2X\u53ef\u4ee5\u88ab\u5316\u7b80\u6210\u4ec0\u4e48

\u4ec5\u4f9b\u53c2\u8003

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

sin2X-cos2X=2sinXcosX-（cos^2X-sin^2X）=2sinXcosX-cos^2X+sin^2X不能再化简了，这种方法行不通。
sin2X-cos2X=√2sin2Xcosπ/4-√2cos2Xsinπ/4=√2sin（2x-π/4）可以化简了，由书上公式还可以化成√2cos（2x+π/4）。答案√2sin（2x-π/4）正确√2cos（2x+π/4）也正确

sin2x-cos2x=根号2*sin(2x-派/4)

sin2X-cos2X鍙互琚鍖栫畝鎴愪粈涔
绛旓細sin2X-cos2X=鈭2sin2Xcos蟺/4-鈭2cos2Xsin蟺/4=鈭2sin锛2x-蟺/4锛夊彲浠ュ寲绠浜嗭紝鐢变功涓婂叕寮忚繕鍙互鍖栨垚鈭2cos锛2x+蟺/4锛夈傜瓟妗堚垰2sin锛2x-蟺/4锛夋纭垰2cos锛2x+蟺/4锛変篃姝ｇ‘

sin2x-cos2x鎬庝箞鍖栫畝
绛旓細sin2x-cos2x鍖栫畝寰椻垰2.sin(2x-蟺/4)銆傝繖涓槸涓夎鍑芥暟寰楀寲绠銆備笁瑙掑嚱鏁版槸鍩烘湰鍒濈瓑鍑芥暟涔嬩竴锛屾槸浠ヨ搴︿负鑷彉閲忥紝瑙掑害瀵瑰簲浠绘剰瑙掔粓杈逛笌鍗曚綅鍦嗕氦鐐瑰潗鏍囨垨鍏舵瘮鍊间负鍥犲彉閲忕殑鍑芥暟銆備篃鍙互绛変环鍦扮敤涓庡崟浣嶅渾鏈夊叧鐨勫悇绉嶇嚎娈电殑闀垮害鏉ュ畾涔夈備笁瑙掑嚱鏁板湪鐮旂┒涓夎褰㈠拰鍦嗙瓑鍑犱綍褰㈢姸鐨勬ц川鏃舵湁閲嶈浣滅敤锛屼篃鏄爺绌跺懆鏈熸х幇...

sin2x-cos2x鎬庝箞鍖栫畝?
绛旓細sin2X-cos2X =鈭2sin2Xcos蟺/4-鈭2cos2Xsin蟺/4 =鈭2sin锛2x-蟺/4锛夊嶈鍗婅鍏紡锛歴in ( 2伪 ) = 2sin伪 路 cos伪 sin ( 3伪 ) = 3sin伪 - 4sin & sup3 ; ( 伪 ) = 4sin伪 路 sin ( 60 + 伪 ) sin ( 60 - 伪 )sin ( 伪 / 2 ) = 卤 鈭( ( 1 - cos伪...

y=sin2x-cos2x鎬庝箞鍖栫畝
绛旓細y =sin2x-cos2x =鈭2.sin(2x-蟺/4)

sin2x-cos2x鐨勫寲绠涓鑳戒笉鑳鎶2鍑烘潵,鐒跺悗鍙樻垚:2(½sin2x-½cos...
绛旓細浼间箮涓嶈兘,濡備笅 涓嶈繃涔熷彲浠ュ彉鎴

sin2x-cos2x鎬庝箞鍖栫畝
绛旓細瑙ｅ寲绠鏄牴2sin(x-鍏/4)

sin2x-cos2x鎬庝箞杞崲涓衡垰2sin(2x-鍏/4),杩欎釜鎷彿閲岀殑鍏/4涓嶇煡閬撴庝箞鏉...
绛旓細鐢ㄨ緟鍔╄鍏紡锛歛sina+bcosa=鈭(a²锛媌²)sin(a+蠁)sin2x锛峜os2x =鈭2脳[(鈭2/2)sin2x锛(鈭2/2)cos2x]=鈭2[sin2xcos(蟺/4)锛峜os2xsin(蟺/4)]=鈭2sin(2x锛嵪/4)

sin2x-cos2x鎬庝箞鍖栨垚asin鐨勫舰寮
绛旓細杈呭姪瑙掑叕寮忥紝鎻愬彇绯绘暟骞虫柟鍜屽紑鏍瑰彿锛屼篃灏辨槸浜屽垎涔嬫牴鍙蜂簩

sin2xcos2x鍙互鍖栬В寰楀灏???
绛旓細1/2sin4x

f(x)=sin2x-cos2x,鍒檉'(x)=?
绛旓細f'(x)=cos2x脳锛2x锛'+sin2x脳锛2x锛夆=2cos2x+2sin2x=2(sin2x+cos2x)鎰挎剰鍖栫畝鍙互缁х画 =2鍊嶆牴鍙2sin(2x+45掳)

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