If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx...

If `y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+\ ddotto\ oo))))` , prove that `(dy)/(dx)=((1+y)cosx+ysinx)/(1+2y+cosx-sinx)`

Text Solution

AI Generated Solution

Topper's Solved these Questions

DIFFERENTIALS, ERRORS AND APPROXIMATIONS
RD SHARMA ENGLISH|Exercise All Questions|107 Videos
DIRECTION COSINES AND DIRECTION RATIOS
RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+ tooo)))),p rov et h a t(dy)/(dx)=((1+y)cosx+ysinx)/(1+2y+cosx-sinx)

Prove that (cosx)/(1-sinx)=(1+cosx+sinx)/(1+cosx-sinx)

If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+\ dotto\ oo))) , prove that (dy)/(dx)=(sinx)/(1-2y) .

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo))) , prove that (dy)/(dx)=(cosx)/(2y-1)

d/dx((1-cosx)/sinx)=

tan^-1((1+cosx)/(sinx))

Prove that (1-sinx)/(cosx)=(cosx)/(1+sinx)

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions

If y=sqrt(x)^(sqrt(x)^(sqrt(x)^dotoo)) , show that (dy)/(dx)=(y^2)/(x(...
Text Solution
|
If y=x+1/(x+1/(x+1/(x+\ dot))) , prove that (dy)/(dx)=y/(2y-x) .
Text Solution
|
If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+\ ddotto\ oo)))) , prove ...
Text Solution
|
If y=sqrt(x+sqrt(x+sqrt(x+\ dotto\ oo))) , prove that (dy)/(dx)=1/(2\ ...
Text Solution
|
If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+\ dotto\ oo))) , prove that (dy)/(d...
Text Solution
|
If y=sqrt(logx+sqrt(logx+sqrt(logx+\ dotto\ oo))) , prove that (2y-1)(...
Text Solution
|
If y=sqrt(tanx+sqrt(tanx+sqrt(tanx+\ dotto\ oo))) , prove that (dy)/(d...
Text Solution
|
If y=sinx^(sinx^(sinx^dotoo)) , prove that (dy)/(dx)=(y^2cotx)/((1-ylo...
Text Solution
|
Prove that : cos 6x=32 cos^6 x -48cos^4 x - 18 cos^2 x -1
Text Solution
|
If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e)) , prove that (dy)/(dx)=e^(x^(...
Text Solution
|
If y=cosx^(cosx^(cosx^dotoo)) , prove that (dy)/(dx)=-(y^2tanx)/((1-yl...
Text Solution
|
Find (dy)/(dx) : x=a{cost+1/2logt a n^2t/2} and y=asint .
Text Solution
|
Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)
Text Solution
|
If x=asec^3thetaa n dy=atan^3theta,fin d(dy)/(dx)a ttheta=pi/3dot
Text Solution
|
Find (dy)/(dx) , when x=a\ cos^3t and y=at .
Text Solution
|
If x=sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)=...
Text Solution
|
If x=sin^(-1)((2t)/(1+t^2)) and y=tan^(-1)((2t)/(1-t^2)),t > 1. Prove ...
Text Solution
|
If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt(...
Text Solution
|
If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...
Text Solution
|
Find (dy)/(dx) , when x=a t^2 and y=2\ a t
Text Solution
|