Proving this trignometric identity

[hms.tech]

Homework Statement

Prove that :

\frac{cos(x)-1}{(1-cos(x))^{3}} = -\frac{1}{4sin^{4}(0.5x)}

Homework Equations

None that I can think of.
Maybe the double angle formula...

The Attempt at a Solution

I couldn't do much in this question :

-\frac{1}{(1-cos(x))^{2}}

 

[micromass]

Things to try: expand (1-\cos(x))^2 and expressing \sin(x/2) in terms of just sin and cos.

 

[ehild]

Yes, use the double angle formula.

ehild

 

[hms.tech]

...and expressing \sin(x/2) in terms of just sin and cos.

What exactly do you mean by that ?

Should I expand it in powers of Sin(x)/Cos(x) ?

 

[Saitama]

What exactly do you mean by that ?

Should I expand it in powers of Sin(x)/Cos(x) ?

Use double angle formula. What is cos(2x) in terms of sin? Similarly, what is cos(x)?