sin2x-2sin²x怎么化简

sin2x-2sin²x怎么化简
sin2x-2sin²x怎么化简

sin2x-2sin²x怎么化简
cos2x=1-2sin²x
可得2sin²x= 1-cos2x
原式= sin2x+cos2x-1
= √2(√2/2*sin2x+√2/2*cos2x)-1
=√2sin(2x+45°)-1

sin2x-2sin²x
=2sinxcosx-2sin²x
=2sinx(cosx-sinx)
=2√2sinx(√2/2*cosx-√2/2sinx)
=2√2sinx(sinπ/4cosx-cossinπ/4sinx)
=2√2sinxsin(π/4-x)