Answer:
(sin^2 w + 1) / cos w.
Step-by-step explanation:
Note: sec w = 1 / cos w and csc w = 1/ sin w.
So we have:
(sec w(1 + csc^2 w)) / (csc^2 w)
= 1/cos w ( 1 + 1/ sin^2 w) / (1 / sin^2 w)
= ( 1/ cos w + 1 / sin^2 w cos w) * sin^2 w
= sin^2 w/ cos w + sin^2 w / (sin^2 w cos w)
= sin^2 w / cos w + 1 / cos w
= (sin^2 w + 1) / cos w.
