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Mathematics
OpenStudy (aravindg):

if x=a(cos t +log tan1/2 t) and y=a sin t ,show that dy/dx=tan t @Physics

OpenStudy (anonymous):

is log = ln or log base 10?

OpenStudy (aravindg):

ln

OpenStudy (anonymous):

plz click on that and help me?

OpenStudy (aravindg):

dont post ur qn here

OpenStudy (anonymous):

Ok then. \[x=a(cost+\ln(\tan(t/2)) \rightarrow dx/dt=a(-sint+0.5\sec^2(t/2)/\tan(t/2))\]\[y=asint \rightarrow dy/dt=acost\]

OpenStudy (anonymous):

what an ugly mess, but i guess that is what you have to do \[\frac{dy}{dx}=\frac{dy}{dt}\frac{dt}{dx}\]

OpenStudy (anonymous):

Sorry about the delay, was just re-checking my work.

OpenStudy (anonymous):

\[a(-sint+0.5\sec^2(t/2)/\tan(t/2)) = a(-sint+\sec(t/2)/2\sin(t/2))\]\[=a(-sint+1/2\cos(t/2)\sin(t/2))\] [Double angle formula for sin]\[=a(-sint+1/sint)\]\[this \implies dy/dx = cost/(-sint+1/sint) = sintcost/(1-\sin^2 t)\]\[1-\sin^2 t = \cos^2t \therefore dy/dx = sintcost/\cos^2 t = sint/cost=tant\] Q.E.D.

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