Question

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)​

Answer 1

(sin^2 w + 1) / cos w.

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.