(Trig) Rewriting using power-reducing formula?

[yue_]

Homework Statement

Rewrite sin^4 xtan^4 x in terms of the 1st power of the cosine.

Homework Equations

sin^2 x=(1-cosx)/2
tan^2 x=(1-cosx)/(1+cosx)

The Attempt at a Solution

For this problem, I tried to rewrite tan^2 x as (sin^2 x/cos^2 x)
But then I ended up with a...cubic function, which made the problem even more complicated. What am I doing wrong here?

 

[SammyS]

The problem you posted was sin⁴(x) tan⁴(x). -- both with the power, 4.

Your answer still has cos³ & cos² .

sin⁴(x)

= (1-cos²(x))sin²(x)

= sin²(x) - cos²(x)sin²(x)

= (1 - cos(2x))/2 - sin²(2x)/4

...