If `x=cos e ctheta-sinthetaa n dy=cos e c^ntheta-sin^ntheta,` then show that `(x^2+4)((dy)/(dx))^2=n^2(y^2+4)dot`

If x=cos ec theta-sin theta;y=cos ec^(n)theta-sin^(n)theta then show that (x^(2)+4)((dy)/(dx))^(2)-n^(2)(y^(2)+4)=0

If x=sec theta-cos theta and y=sec^(n)theta-cos^(n)theta then show that (x^(2)+4)((dy)/(dx))^(2)=n^(2)(y^(2)+4)

If P_n=cos^ntheta+sin^ntheta, show that : 2P_6-3P_4+1=0 .

If y = a sin x + b cos x , show that y^2+((dy)/(dx))^2=a^2+b^2

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 x= e^(theta )(sin theta - cos theta ) , y= e^(theta ) ( sin theta + cos theta ) then (dy)/(dx) at theta =(pi)/(4) is