化简f(x)=2((cosX)cosX)+2sinXcosX
问题描述:
化简f(x)=2((cosX)cosX)+2sinXcosX
答
f(x)=2cos²x-1+2sinxcosx+1
=cos2x+sin2x+1
=√2(√2/2*sin2x+√2/2cos2x)+1
=√2(sin2xcosπ/4+cos2xsinπ/4)+1
=√2sin(2x+π/4)+1