let-give-x-0-2pi-and-a-R-b-R-prove-that-pi-x-2-arctan-sinx-1-cosx-2-prove-that-arctan-a-arctan-b-a-b-3-let-0-pi-2-x-2pi-r-0-1-prove-that-x-r-pi-x-2- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 35610 by abdo mathsup 649 cc last updated on 21/May/18 letgivex∈]0,2π[anda∈R,b∈Rprovethatπ−x2=arctan(sinx1−cosx)2)provethat∣arctan(a)−arctan(b)∣⩽∣a−b∣3)letθ∈]0,π2[,x∈[θ,2π−θ],r∈[0,1[provethat∣φ(x,r)−π−x2∣⩽1−r(1−cosθ)2 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: let-r-0-1-and-x-R-and-x-r-arctan-rsinx-1-r-cosx-1-prove-that-x-x-r-n-1-r-n-cos-nx-2-prove-that-x-r-n-1-r-n-sin-nx-n-Next Next post: let-h-t-e-t-e-t-and-for-n-0-we-put-h-n-t-nh-nt-calculate-h-n-t-dt- Leave a Reply Cancel replyYour email address will not be published.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.
![let give x∈]0,2π[ and a ∈R,b∈ R prove that ((π−x)/2) = arctan(((sinx)/(1−cosx))) 2) prove that ∣arctan(a)−arctan(b)∣≤∣a−b∣ 3)letθ ∈]0,(π/2)[ , x ∈[θ,2π−θ] , r∈[0,1[ prove that ∣ϕ(x,r) −((π−x)/2)∣≤ ((1−r)/((1−cosθ)^2 ))](https://www.tinkutara.com/question/Q35610.png)