sin2x减cos2x

卫翟顷3270sin2x - cos2x=根号2sin(2x - π/4) 为什么啊 -
花饺柏15552125704 ______[答案] sin2x-cos2x=√2(√2/2sin2x-√2/2cos2x) =√2(sin2xcosπ/4-cos2xsinπ/4) =√2sin(2x-π/4)

卫翟顷3270求函数y=sin2x - cos2x的最大值.并写出函数取最大值时自变量x值的集合 -
花饺柏15552125704 ______[答案] 因为y=sin2x-cos2x=√2sin(2x-π/4),所以函数y=sin2x-cos2x的最大值是√2; 当函数取最大值时,2x-π/4=π/2+2kπ,k∈Z,即:2x=3π/4+2kπ,k∈Z, 故:x=3π/8+kπ,k∈Z,

卫翟顷3270函数f(x)=sin2x - cos2x的最小正周期是( ) -
花饺柏15552125704 ______[选项] A. π B. 2π C. 4π

卫翟顷3270求y=sin2x - cos2x的周期、最值与单调区间 -
花饺柏15552125704 ______ 解:y=sin2x-cos2x=√2sin(2x-π/4) 周期T=2π/2=π 最值:最大值为√2,最小值为-√2 单调性:①-π/2+2kπ≤2x-π/4≤π/2+2kπ 解得:-π/8+kπ≤x≤3π/8+kπ 当-π/8+kπ≤x≤3π/8+kπ单调增加 ②π/2+2kπ≤2x-π/4≤3π/2+2kπ 解得:3π/8+kπ≤x≤7π/8+kπ 当3π/8+kπ≤x≤7π/8+kπ单调减小

卫翟顷3270函数y=sin2x - cos2x的导数是 (要详细的过程,最好用纸写下来) -
花饺柏15552125704 ______ ∵y=sin2x-cos2x=-cos2x, ∴y′=(-cos2x)′=(sin2x)?(2x)′=2sin2x. 故答案为:2sin2x.

卫翟顷3270函数 sin2x - cos2x的最小正周期是( ) -
花饺柏15552125704 ______ sin2x-cos2x=(根号2)sin(2x θ)(θ是个辅助角,没有关系)所以最小正周期 = 2π÷2=π

卫翟顷3270sin2x - cos2x=根号2·sin(2x - π/4)?怎么变的 -
花饺柏15552125704 ______[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)

卫翟顷3270y=sin2x - cos2x的最小正周期如题 -
花饺柏15552125704 ______[答案] π/2 y=sin2xcos2x =1/2(2sin2xcos2x) =1/2sin4x 就是半个圆周率

卫翟顷3270sin2x - cos2x
花饺柏15552125704 ______ 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.

卫翟顷3270sin2x - 如何变成cos2x -
花饺柏15552125704 ______[答案] 不可能吧,求导也不对啊