Question

given y=theta-cos theta and x=sin theta. Show that d^2x/dy^2 =sec^2 theta (tan theta + sec theta)

Answer 1

y = θ - cosθ and
x = sinθ

before I do this, confirm that this is what you actually meant,
and confirm you are not missing some trig operator in front of
that first θ

Answer 2

Yes I didn’t miss any trig operator