根号2*sinx=sin2x+cos2x 求x

题目

根号2*sinx=sin2x+cos2x 求x

答案

根号2*sinx=sin2x+cos2x
√2sinx=√2sin(2x+π/4)
(1)2kπ+x=2x+π/4
x=2kπ-π/4；k∈Z
(2)2kπ+π-x=2x+π/4
3x=2kπ+3π/4
x=2kπ/3+π/4；k∈Z