Given the equation f(cos x)=cot x/sin x, find a formula for f(x)

Question

anonymous · Answer

First we evaluate cot x.
From trig you should remember that cot x=cos x/sin x
Substitute cot in the given equation to get
f(cosx)=cos x/(sin x)(sin x)
since equate f(cos x) to f(x) we substitute cos x with x in our given equation
so our formula for f(x) should be 
f(x)=x/(sin x)^2
let me know if you have any questions

anonymous · Answer

$$f(cosx)=1/(tanxsinx)=\frac{1}{\frac{sinx}{cosx}{sinx}}=\frac{cosx}{\sin^2x}$$Using a standard trig identity, this becomes:$$f(cosx)=\frac{cosx}{1-\cos^2x}$$

myininaya · Answer

$$f(cosx)=\frac{cotx}{sinx}=cotx \div sinx$$ 
$$= \frac{cosx}{sinx} \times \frac{1}{sinx}$$
$$=\frac{cosx}{\sin^2x}$$
so
$$f(x)=\frac{x}{\sin^2x}$$

anonymous · Answer

Let u=cosx, then,$$f(u)=\frac{u}{1-u^2}$$But we want it in terms of x, and $$x=\cos^{-1} u$$Inputting:$$f(x)=f(\cos^{-1} u)=\frac{x}{1-x^2}$$

myininaya · Answer

or maybe the function could be 
$$f(x)=\frac{x}{1-x^2}$$ based on what eseidl has
function could be many things