Find the slope of the normal to the curve `x = 1 - a sin theta`, `y = b cos^2 theta at theta = pi/2`

Find the slope of the tangent of the following curve at the given point: x=tantheta y=cot theta at theta=pi/4

Find cos^2 theta - sin^2 theta . .

Find dy/dx : x = r cos theta, y = r sin theta

Solve 2cos^2 theta+3 sin theta=0

Find (d^2y)/(dx^2) : x = a(theta - sintheta), y = a(1 - costheta) at theta = (pi)/2 .

Find dy/dx : x = a sec^2 theta, y = b tan^3 theta

Solve 7 cos^2 theta+3 sin^2 theta=4

Find dy/dx : x = cos theta + sin theta, y = sin theta - theta cos theta

Eliminate theta , x=a cos^3theta , y=b sin^3theta