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

Question

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

anonymous · Answer

is log = ln or log base 10?

aravindg · Answer

ln

anonymous · Answer

http://imageshack.us/photo/my-images/338/unledvgp.png/

anonymous · Answer

plz click on that and help me?

aravindg · Answer

dont post ur qn here

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

$$a(-sint+0.5\sec^2(t/2)/\tan(t/2)) = a(-sint+\sec(t/2)/2\sin(t/2))$$$$=a(-sint+1/2\cos(t/2)\sin(t/2))$$  [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.