Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 54586 by arvinddayama00@gmail.com last updated on 07/Feb/19

(√(1−x^2 )) + (√(1−y^2 )) = a(x−y)  prove that  (dy/dx)=(√((1−y^2 )/(1−x^2 )))

1x2+1y2=a(xy)provethatdydx=1y21x2

Answered by tanmay.chaudhury50@gmail.com last updated on 07/Feb/19

x=sinp  y=sinq  (dx/dp)=cosp   (dy/dq)=cosq  (dy/dx)=((cosqdq)/(cospdp))  (√(1−x^2 )) +(√(1−y^2 )) =a(x−y)  cosp+cosq=a(sinp−sinq)  a=((2cos((p+q)/2)×cos((p−q)/2))/(2cos((p+q)/2)sin((p−q)/2)))  tan((p−q)/2)=(1/a)  sec^2 (((p−q)/2))((((dp/dx)−(dq/(dx )))/2))=0  so (dp/dx)−(dq/dx)=0  so (dp/dq)=1  now(dy/dx)=((cosq)/(cosp))×(dq/dp)[(dq/dp)=1]  (dy/dx)=((cosq)/(cosp))=((√(1−y^2 ))/(√(1−x^2  )))

x=sinpy=sinqdxdp=cospdydq=cosqdydx=cosqdqcospdp1x2+1y2=a(xy)cosp+cosq=a(sinpsinq)a=2cosp+q2×cospq22cosp+q2sinpq2tanpq2=1asec2(pq2)(dpdxdqdx2)=0sodpdxdqdx=0sodpdq=1nowdydx=cosqcosp×dqdp[dqdp=1]dydx=cosqcosp=1y21x2

Commented by arvinddayama00@gmail.com last updated on 08/Feb/19

any or solution

anyorsolution

Commented by tanmay.chaudhury50@gmail.com last updated on 08/Feb/19

trying by other method

tryingbyothermethod

Terms of Service

Privacy Policy

Contact: info@tinkutara.com