求证:cosx+sinx=根号2cos(x-π/4)
问题描述:
求证:cosx+sinx=根号2cos(x-π/4)
答
两边同时平方 然后右侧化消次就行了
答
展开即得
答
cosx+sinx
=√2[((√2/2)cosx+(√2/2)sinx]
=√2[cosxcos(π/4)+sinxsin(π/4)]
=√2cos(x-π/4)
得证