已知@,p均为锐角,且cos(@+p)=sin(@-p),则sin@-cos@=?

已知@,p均为锐角,且cos(@+p)=sin(@-p),则sin@-cos@=?
已知@,p均为锐角,且cos(@+p)=sin(@-p),则sin@-cos@=?

已知@,p均为锐角,且cos(@+p)=sin(@-p),则sin@-cos@=?
变形得cosacosp-sinasinp=sinacosp-cosasinp cosacosp+cosasinp=sinacosp+sinasinp
cosa(cosp+sinp)=sina(cosp+sinp)
cosa=sina
sina-cosa=0

sin(θ-p)=cos[π/2-(θ-p)]=cos(π/2+p-θ)=cos(θ+p)
π/2+p-θ=θ+p
θ=π/4
sinθ-cosθ=0