Question

Which of the following is equivalent to the given expression?
(Sin^2x)/(1-cosx)
a. tanx + sinx b. cscx + cotx c. cotx sinx + tanx d.1 + cosx e. tanx cotx - cosx

Answer 1

start with the numerator

\[\sin^2(x) + \cos^2(x) = 1~~~~~then~~~~~\sin^2(x) = 1 - \cos^2(x)\]

which is the difference o 2 squares.

( (1 - cos(x))(1 + cos(x))

make the substitution and simplify