证明sinθ+cosθ=根号2sin(θ+π/4)

问题描述:

证明sinθ+cosθ=根号2sin(θ+π/4)

sin和cos前的系数均为1,提取出根号2(因为sinπ/4=cosπ/4=根号2)
一般的,对于asinθ+bcosθ均可提取根号下(a^2+b^2)

右式=根号2sin(θ+π/4)=根号2(sinθcosπ/4+cosθsinπ/4)=sinθ+cosθ=左式
证毕