cos2x-sin2x可以直接用辅助角公式吗 如果不行,应该怎么化简
cos2x-sin2x=cosx^2-sinx^2-2sinxcosx=(cosx-sinx)^2-2sinx^2
=(cosx+(-1+2^0.5)sinx)(cosx-(1+2^0.5)sinx)
绛旓細cos2x-sin2x=cosx^2-sinx^2-2sinxcosx =(cosx-sinx)^2-2sinx^2 =(cosx+(-1+2^0.5)sinx)(cosx-(1+2^0.5)sinx)
绛旓細cos2x-sin2x=cosx^2-sinx^2-2sinxcosx =(cosx-sinx)^2-2sinx^2 =(cosx+(-1+2^0.5)sinx)(cosx-(1+2^0.5)sinx)
绛旓細cos2x-sin2x =鈭2脳[cos2x*(鈭2/2)-sin2x*(鈭2/2)]=鈭2脳[cos2x*cos(蟺/4)-sin2x*sin(蟺/4)]=鈭2cos[2x+(蟺/4)]
绛旓細cos2x锛sin2x=鈭2cos(2x锛嬒/4)
绛旓細cos2x-sin2x =鈭2*(cos2x*鈭2/2 - sin2x*鈭2/2)=鈭2*[cos2x*cos(蟺/4) - sin2x*sin(蟺/4)]=鈭2*cos(2x+ 蟺/4)
绛旓細杩欎釜鐭ヨ瘑鐐瑰彨杈呭姪瑙掑叕寮忥紝涔熷氨鏄綑寮︾殑涓よ鍜屽叕寮忕殑閫嗙敤銆
绛旓細鐢ㄨ緟鍔╄鍏紡鍖栫畝 cos2x-sin2x=鏍瑰彿2锛堟牴2/2cos2x-鏍2/2sin2x)=鏍2(cos蟺/4cos2x-sin蟺/4sin2x锛=鏍2cos锛2x+蟺/4)
绛旓細cos(伪+尾)=cos伪cos尾-sin伪sin尾 cos2x=cos(x+x)=cos²x-sin²x
绛旓細cos²x-sin2x=cos²x-2sinxcosx =(cos²x-2sinxcosx)/(sin²x+cos²x) 鍒嗗瓙鍒嗘瘝鍚岄櫎cos²x =(1-2tanx)/(tan²x+1)鏁板鐖卞ソ鑰呭洟闃熶负鎮ㄨВ绛旓紝濡傛灉涓嶆噦锛岃杩介棶~~绁濆涔犺繘姝ワ紒
绛旓細鍒╃敤涓よ鍜岀殑浣欏鸡鍏紡cos2X = cos(X+X) = cosXcosX- sinXsinX = cos^2 X- sin^2 X = 2cos^2 X- 1=1 - 2sin^2 X
