If `x=sectheta-tanthetaa n dy=cos e ctheta+cottheta,` then prove that `x y+1=y-xdot`

If x=sectheta-tantheta , and y=cosectheta+cottheta , then

If x=sectheta "and " y=cosec theta +cottheta , then prove that xy+1=y-x .

If cottheta+tantheta=xand sectheta-costheta=y , then

Prove that:sqrt((1+costheta)/(1-costheta))={cos e ctheta+cottheta,if0

If p\ a n d\ p ' be the perpendicular form the origin upon the straight lines x s e ctheta+y cos e ctheta=a\ a n d\ xcostheta-y s intheta=acos2thetadot Prove that : 4p^2+p^'^2=a^2\ dot

If e^x+e^y=e^(x+y) then prove that dy/dx =- e^(y-x)

If x = e^(x//y) , then prove that (dy)/(dx) = (x-y)/(xlogx) .

if e^(-y)y=x then prove that (dy)/(dx)=(y)/(x(1-y))

If y=(e^(x))/(x) then prove that x(dy)/(dx)=y (x-1)