prove-that-0-pi-4-sin-x-cos-x-1-sin-x-cos-x-dx-2-cot-1-2- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 163158 by mnjuly1970 last updated on 04/Jan/22 provethat∫0π4sin(x)+cos(x)1+sin(x)cos(x)dx=2.cot−1(2)−−−−− Answered by mahdipoor last updated on 04/Jan/22 getsinx−cosx=3u{3du=(cosx+sinx)dx3u2=sin2x+cos2x−2sinx.cosx⇒1−3u22=sinx.cosx⇒∫0π/4sinx+cosx1+sinx.cosxdx=∫−1/303du1+1−3u22=2∫−1/30du1−u2=[2sin−1u+C]−1/30=−2sin−1(−13)=2sin−1(13)ifsinx=13⇒cotx=2⇒2sin−1(13)=2cot−1(2) Commented by mnjuly1970 last updated on 04/Jan/22 bravosirmahdipoor Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: show-that-cos-x-y-cos-x-y-1-tanxtany-1-tanxtany-Next Next post: let-f-x-arctan-x-2-3-1-calculate-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-3-calculate-0-1-f-x-dx- Leave a Reply Cancel replyYour email address will not be published.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.