If ` x = a cos theta , y = b sin theta ` , then prove that ` ( d^(3) y)/( dx^(3)) = - ( 3 b)/( a^(3)) cosec^(4) theta cot theta `

If x = a(1+ cos theta), y = a (theta + sin theta) , then (d^(2)y)/(d x^(2)) at theta = (pi)/(2) is

If x= alpha cos ^(3) theta and y = alpha sin ^(3) theta, then 1 + ((dy)/(dx)) ^(2) is

If x=acos^3theta , y=asin^3theta Find (d^2y)/dx^2 .

If x=acos^3theta and y=asin^3theta . Prove that 1+(dy/dx)^2=sec^2theta .

Find dy/dx if x=2cos^3theta , y=2sin^3theta .

Evaluate |[cos theta, -sin theta], [sin theta, cos theta]|

If cos theta, sin phi, sin theta are in G.P., then prove that roots of x^(2)+2 cot phi x+1=0 are real

The parametric form of the ellipse 4 (x +1) ^(2) + (y-1) ^(2) = 4 is a) x = cos theta -1 , y =2 sin theta -1 b) x = 2 cos theta-1 , y =2 sin theta -1 c) x = cos theta - 1, y = 2 sin theta + 1 d) x = cos theta +1, y =2 sin theta +1