Simplify and write the trigonometric expression in terms of sine and cosine: cot(-x)cos(-x)+sin(-x)=-1/f(x)=f(x)=____________

Question

I've tried everything, I think that the "-1/f(x)" part is screwing up my answer but I'm not sure what it's asking me to do with that?

Answer 1

I will "simplify and write the trigonometric expression in terms of sine and cosine"
the part "=-1/f(x)=f(x)=____________ "
makes little sense to me

cot(-x)cos(-x)+sin(-x)
= (cos(-x))/sin(-x))(cos(-x) + sin(-x)
= (cosx/-sinx)(cosx) - sinx
= - cos^2 x/sinx - sin^2 x/sinx
= -(cos^2 x + sin^2 x)/sinx
= -1/sinx

Answer 2

thank you, the answer is just:
=sin(x)

Answer 3

No, it isn't
the simplification of the expression is
-1/sinx, as you can see from my steps

however,
if -1/f(x) = -1/sinx
then f(x) = sinx