Prove-that-x-pi-4-n-0-cos-x-2-n-cos-pi-2x-2-n-1-2-4cos2x-pi-pi-4x- Tinku Tara June 4, 2023 Differentiation 0 Comments FacebookTweetPin Question Number 83209 by ~blr237~ last updated on 28/Feb/20 Provethat∀x≠π4,∏∞n=0(cos(x2n)+cos(π−2x2n+1)2)=4cos2xπ(π−4x) Answered by mind is power last updated on 28/Feb/20 cos(a)+cos(b)=2cos(a+b2)cos(a−b2)cos(π2n+2)cos(4x−π2n+2)∏Nn=0cos(a2n)=1sin(a2N)∏Nn=0cos(a2n).sin(a2N)⇒∏Nn=0cos(a2n)=sin(2a)2N+1sin(a2N)limN→0=sin(2a)2a∏Nn=0cos(π4.2n)=sin(π2)2N+1sin(π4.2N)→2π∏Nn=0cos(4x−π2n.2)=sin(4x−π2)(4x−π2)=2sin(2x−π2)4x−π=2cos(2x)π−4x⇒weget.2π.2cos(2x)π−4x=4cos(2x)π(π−4x) Commented by ~blr237~ last updated on 28/Feb/20 nicesir Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: t-1-t-ln-x-dx-Next Next post: Question-17675 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.