Rewriting trigonometric identities

[aghtar]

Hey guys, I have this problem that I got stuck with,

Rewrite sin²(4x) as a function of cot(4x).

This is what I came up with but got stuck:

sin(4x) = 1-cos²(4x)
= 1-(cos(4x))²
= 1-(sin(4x)/tan(4x))²
= 1-(sin(4x)/(1/cot(4x)))²
= 1-((1/csc(4x))/(cot(4x)/1))²

then got stuck, don't really know if what I did was possible, but I was using the identities as I could, any help is appreciated.

 

[Deleted member 4993]

Hey guys, I have this problem that I got stuck with,

Rewrite sin²(4x) as a function of cot(4x).

This is what I came up with but got stuck:

sin²(4x) = 1-cos²(4x)
= 1-(cos(4x))²
= 1-(sin(4x)/tan(4x))²
= 1-(sin(4x)/(1/cot(4x)))²
= 1-((1/csc(4x))/(cot(4x)/1))²

then got stuck, don't really know if what I did was possible, but I was using the identities as I could, any help is appreciated.

Now use

cot²(Θ) = cosec²(Θ) - 1