sin2x-cos2x等于多少

益军轰4436三角函数的化简,y=sin 2x - cos2x,怎样化简啊?求这个函数的周期 -
弘娇姣18719866128 ______ 思路:化为一个三角函数, 具体如: y= sin2x - cos2x = sin2x - sin(∏/2-2x) = 2cos[(2x+∏/2-2x)/2]*sin[(2x-∏/2+2x)/2] = 2·√2/2·sin(4x-∏/2) = -√2·cos4x, 所以周期就是: T = 2∏/ω = 2∏/4 = ∏/2 .

益军轰4436为什么等于sin2x - cos2x? -
弘娇姣18719866128 ______ 依据公式: sin2x=2sinxcosx cos2x=cos²x-sin²x

益军轰4436已知sinx - cosx=1/2,则sin2x - cos2x= -
弘娇姣18719866128 ______[答案] sinx-cosx=1/2 平方 (sinx)^2+(cosx)^2-2sinxcosx=1/4 1-2sinxcosx=1/4 2sinxcosx=3/4 sin2x=3/4 (sinx+cosx)^2=(sinx-cosx)^2+4sinxcosx (sinx+cosx)^2=(1/2)^2+2*3/4 (sinx+cosx)^2=1/4+6/4 (sinx+cosx)^2=7/4 sinx+cosx=±√7/2 sin2x-cos2x =sin2x-[...

益军轰4436sin2x - cos2x=√2si(2x - π/4)怎么推倒出来的,sin2x - cos2x=√2sin(2x - π|4)这把对了! -
弘娇姣18719866128 ______[答案] sin2x-cos2x = √2[sin2x(√2/2) - (√2/2)cos2x] = √2[sin2xcos(π/4) - sin(π/4)cos2x] = √2sin(2x - π/4)

益军轰4436sin2x - cos2x -
弘娇姣18719866128 ______ f(x)=sin2x—cos2x=sin2xcos(π/4)—cos2xsin(π/4)=√2sin(2x-π/4) 因为函数y=sinx的周期是π 所以f(x)单调递增区间:(2kπ-π/2)≤(2x-π/4)<(2kπ+π/2) (k为整数) 即(kπ-π/8)≤x<(kπ+3π/8) f(x)单调递减区间:(2kπ+π/2)≤(2x-π/4)<(2kπ+3π/2) (k为整数) 即(kπ+3π/8)≤x<(kπ+7π/8) 所以函数f(x)在[kπ-π/8,kπ+3π/8)为递增,在[kπ+3π/8,kπ+7π/8)为递减.

益军轰4436求函数y=sin2x - cos2x的最大值和最小值 -
弘娇姣18719866128 ______ ∵y=sin2x-cos2x = 2 ( 2 2 sin2x- 2 2 cos2x) = 2 sin(2x- π 4 ), ∴当sin(2x- π 4 )=1时,ymax= 2 , 当sin(2x- π 4 )=-1时,ymin=- 2 .

益军轰4436函数y=sin2x - cos2x的导数是 (要详细的过程,最好用纸写下来) -
弘娇姣18719866128 ______ ∵y=sin2x-cos2x=-cos2x, ∴y′=(-cos2x)′=(sin2x)?(2x)′=2sin2x. 故答案为:2sin2x.

益军轰4436sin2x - cos2x=2 求 x? -
弘娇姣18719866128 ______ 和差化积公式:sin2x-cos2x=2 sin2x+sin(2x-π/2)=22*sin(2x-π/4)cos(π/4)=2 sin(2x-π/4)=根号2 无解

益军轰4436sin2x - cos2x=根号2·sin(2x - π/4)?怎么变的 -
弘娇姣18719866128 ______[答案] sin2x-cos2x=根号2·(sin2x·根号2/2-cox2x·根号2) =根号2·(sin2x·cosπ/4-cos2x·sinπ/4) =根号2·sin(2x-π/4)(逆用差角的正弦公式)

益军轰4436Sin2X - Cos2X化简后=多少?
弘娇姣18719866128 ______ 根号二倍Sin(2x-拍/4)