Simplify the function

Question

Simplify the function

f(x)=(cos^(2)x-sin^(2)x)/(1-cos^(2)x)

Answer 1

1-cos^2x = sin^2x

(cos^2 - sin^2x)/sin^2x

= cos^2x/sin^2x - 1

=cot^2(x) -1

or alternatively with a double angle formula

cos^2x - sin^2x = cos2x

then the expression = cos2x/sin^2x