函数f(x)=sin2x-cos2x,怎么化简到f(x)=√2sin(2x-π/4)的..

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函数f(x)=sin2x-cos2x,怎么化简到f(x)=√2sin(2x-π/4)的..
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函数f(x)=sin2x-cos2x,怎么化简到f(x)=√2sin(2x-π/4)的..
函数f(x)=sin2x-cos2x,怎么化简到f(x)=√2sin(2x-π/4)的..

函数f(x)=sin2x-cos2x,怎么化简到f(x)=√2sin(2x-π/4)的..
f(x)=sin2x-cos2x
=√2*[sin2x*(√2)/2 - cos2x*(√2)/2]
=√2*[sin2x*cos(π/4) -cos2x*sin(π/4)]
=√2*sin(2x-π/4)