y=2cos(2x+π/3)+1 =2cos2xcosπ/3-2sin2xsinπ/3+1 =cos2x-√3sin2 接下去怎么化简

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 09:08:25

y=2cos(2x+π/3)+1 =2cos2xcosπ/3-2sin2xsinπ/3+1 =cos2x-√3sin2 接下去怎么化简
y=2cos(2x+π/3)+1 =2cos2xcosπ/3-2sin2xsinπ/3+1 =cos2x-√3sin2 接下去怎么化简

y=2cos(2x+π/3)+1 =2cos2xcosπ/3-2sin2xsinπ/3+1 =cos2x-√3sin2 接下去怎么化简
y = 2 cos ( 2x + π/3 ) + 1
= 2 cos2x cosπ/3 - 2 sin2x sinπ/3 + 1
= cos2x - √3 sin2x + 1
= 2cos²x - 1 - 2√3 sinx cosx +1
= cosx ( 2 cosx - 2√3 sinx )
= 4cosx ( 1/2 cosx - √3/2 sinx )
= 4cosx cos( x + π/3 )

=cos2x-√3sin2 x=2(1/2cos2x-√3/2sin2x)=2sin(2π/3+2x)