化简f(x)=cos^2(x+π/12)+1/2sin2x

化简f(x)=cos^2(x+π/12)+1/2sin2x
化简f(x)=cos^2(x+π/12)+1/2sin2x

化简f(x)=cos^2(x+π/12)+1/2sin2x
f(x)=cos^2(x+π/12)+1/2sin2x
=1/2*[1+c0s(2x+π/6)]+1/2sin2x
=1/2+1/2(cos2xcosπ/6-sin2xsinπ/6)+1/2sin2x
=1/2+1/2cos2xcosπ/6-1/4sin2x+1/2sin2x
=1/2+1/2cos2xcosπ/6+1/4sin2x
=1/2+1/2(cos2xcosπ/6+sin2xsinπ/6)
=1/2+1/2cos(2x-π/6)
= 1/2[1+cos(2x-π/6)]
=cos^2(x-π/12)