Derive the identity 1 + cot ^2 theta = csc^2 theta by dividing x^2 + y^2 = r^2 by y^2

Answer 1

This must be in reference to a right-angled triangle in standard position with sides x, y, and r
so that sinØ = y/r, cosØ = x/r and tanØ = y/x
You should also know the three reciprocal identities.
x^2 + y^2 = r^2
divide each term by y^2
x^2/y^2 + 1 = r^2/y^2
or
cot^2 Ø + 1 = csc^2 Ø