Use cos2x to derive sin^2(x) in terms of linear powers of common trig functions

Question

i have no clue how to approach this problem, also not sure what it is even asking for.

Answer 1

I am with you; I am not sure exactly what this question is asking.

 

cos 2x = cos² x - sin² x = 1 - 2 sin²x

 

sin² x = (1/2)(1 - cos 2x)

 

If something further is required, you could expand cos 2x as a Taylor series.  Let me know if you need something further.