f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
f(x)=1/2cos 2x+√3/2sin 2x+2(sin x-cos x)(xin x+cos x)
=1/2cos 2x+√3/2sin 2x-2(cos^2 x-sin^2 x)
=1/2cos 2x+√3/2sin 2x-2cos 2x
=-3/2cos 2x+√3/2sin 2x
=√3(1/2sin 2x-√3/2cos 2x)
=√3sin(2x-π/3)
f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
f(x)=1/2cos 2x+√3/2sin 2x+2(sin x-cos x)(xin x+cos x)
=1/2cos 2x+√3/2sin 2x-2(cos^2 x-sin^2 x)
=1/2cos 2x+√3/2sin 2x-2cos 2x
=-3/2cos 2x+√3/2sin 2x
=√3(1/2sin 2x-√3/2cos 2x)
=√3sin(2x-π/3)