求证:cosx+sinx=根号2cos(x-π/4)

问题描述:

求证:cosx+sinx=根号2cos(x-π/4)

两边同时平方 然后右侧化消次就行了

展开即得

cosx+sinx
=√2[((√2/2)cosx+(√2/2)sinx]
=√2[cosxcos(π/4)+sinxsin(π/4)]
=√2cos(x-π/4)
得证