将f(x)=sinxcosx+cos²x化成标准三角函数

问题描述:

将f(x)=sinxcosx+cos²x化成标准三角函数

f(x)=1/2*sin2x+(1+cos2x)/2
=1/2(sin2x+cos2x)+1/2
=1/2(sin2x+cos2x)+1/2
=√2/2(√2/2*sin2x+√2/2cos2x)+1/2
=√2/2(sin2xcosπ/4+cos2xsinπ/4)+1/2
=√2/2sin(2x+π/4)+1/2