怎样使f(x)=sinx+cosx=√2*sin(x+π/4)

问题描述:

怎样使f(x)=sinx+cosx=√2*sin(x+π/4)

f(x)=sinx+cosx=√2(√2/2sinx+√2/2sinxcosx) -------(提一个√2出来)
=√2(sinxcosπ/4+cosxsinπ/4)-(把(√2/2分别变为cosπ/4,sinπ/4)
=√2*sin(x+π/4) ------------------ (两角和正弦公式)