(1-cos2x)+sin2x=根号2(sin2x cosπ/4-cos2x sinπ/4)+1 这个是怎么化简得的?
问题描述:
(1-cos2x)+sin2x=根号2(sin2x cosπ/4-cos2x sinπ/4)+1 这个是怎么化简得的?
答
(1-cos2x)+sin2x
=1-cos2x+sin2x
=sin2x-cos2x+1
=√2(√2/2*sin2x-√2/2*cos2x)+1
=√2(sin2x cosπ/4-cos2x sinπ/4)+1
=√2sin(2x-π/4)+1
答
sin2x-cos2x
=√2(sin2x*√2/2-cos2x*√2/2)
=√2(sin2xcosπ/4-cos2xsinπ/4)
=√2sin(2x-π/4)
这里用到 sinπ/4=cosπ/4=√2/2