函数f(x)=2cosx(sinx-cosx)+1化为y=Asin(ωx+φ)形式,

函数f(x)=2cosx(sinx-cosx)+1化为y=Asin(ωx+φ)形式,
函数f(x)=2cosx(sinx-cosx)+1化为y=Asin(ωx+φ)形式,

函数f(x)=2cosx(sinx-cosx)+1化为y=Asin(ωx+φ)形式,
f(x)=2cosx(sinx -cosx) +1
=2sinxcosx -2cos²x +1
=sin(2x) -[1+cos(2x)] +1
=sin(2x) -cos(2x)
=√2[sin(2x)(√2/2) -cos(2x)(√2/2)]
=√2sin(2x-π/4)

F(x)=2cosx(sinx -cosx) +1
=2sinxcosx -2cos2x +1
=sin(2x) -[1+cos(2x)] +1
=sin(2x) -cos(2x)
=√2[sin(2x)(√2/2) -cos(2x)(√2/2)]
=√2sin(2x-π/4)