" If "x=a cos^(3)theta,y=b sin^(3)theta," prove that "((x)/(a))^(2 beta)+((y)/(b))^(2/3)=1

If x=a cos^(3)theta,y=b sin^(3)theta, then

If x=acos^(3)theta and y = bsin^(3)theta , prove that ((x)/(a))^(2//3)+((y)/(b))^(2//3)=1.

Find the blanks. (i) If x=a cos^(3)theta,y=b sin^(3)theta then ((x)/(a))^(2/3)+((y)/(b))^(2/3)=ul(P) (ii) if x=a sec theta cos phi,y=b sec theta sin phi and z=c tan theta then (x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))=ul(Q) (iii) If cos A+cos^(2)A=1 ,then sin^(2)A+sin^(4)A=ul(R)

If alpha,beta are the intercepts made on the axes by the tangent at any point of the curve x=a cos^(3)theta and y=b sin^(3)theta, prove that (alpha^(2))/(a^(2))+(beta^(2))/(b^(2))=1

If x = a cos^3 theta, y = b sin^3 theta , then

x=a cos^(3)theta,y=b sin^(3)theta : ((x)/(a))^(2/3)+((y)/(b))^(2/3)=1

If x=cos theta,y sin^(3)theta, prove that y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=3sin^(2)theta(5cos^(2)theta-1)

If x= a cos^(3) theta, y= b sin^(3) theta, " then "(dy)/(dx)= (b)/(a) tan theta .

If x = a cos ^(3) theta and y = b sin ^(3) theta , then the value of ((x)/(a))^(2//3) + ((y)/(b))^(2//3)

If x=a cos theta,y=b sin theta, show that (d^(2)y)/(dx^(2))=-(b^(4))/(a^(2)y^(3))