Simplify:
csc^2 x sec x / sec^2 x + csc^2 x
sec^2 + csc^2 = 1/cos^2 + 1/sin^2 = (sin^2+cos^2)/(sin^2 cos^2) = 1/(sin^2 cos^2)
csc^2 sec = 1/(sin^2 cos) = cos/(sin^2 cos^2)
so , doing the division, we end up with just
cos x
csc^2 x sec x / sec^2 x + csc^2 x
csc^2 sec = 1/(sin^2 cos) = cos/(sin^2 cos^2)
so , doing the division, we end up with just
cos x