试证明√2cos(x-π/2)=sinx+cosx
问题描述:
试证明√2cos(x-π/2)=sinx+cosx
答
∵cos(x-π/2)=cosx·cosπ/2-sinx·sin(-π/2)=sinx∴√cos(x-π/2)=√2sinx所以证明不了.本题应是证明√2cos(x-π/4)=sinx+cosx∵sinx+cosx=√2[cosx·cosπ/4+sinx·sinπ/4]又∵cos(A+B)=cosAcosB-sinAsinB∴sin...