How to rewrite the provided sum in another form?

[needingtoknow]

Homework Statement

How to get from

Sum of 2(cos((3pi)/(2^(k+1)))sin(pi/(2^(k+1)))) from k = 1 to infinity

to

Sum of sin((4pi)/(2^(k+1))) - sin((2pi)/(2^(k+1))) from k = 1 to infinity

The two expressions are equivalent. I need help getting from the first expression to the second.

 

[LCKurtz]

Homework Statement

How to get from

Sum of 2(cos((3pi)/(2^(k+1)))sin(pi/(2^(k+1)))) from k = 1 to infinity

to

Sum of sin((4pi)/(2^(k+1))) - sin((2pi)/(2^(k+1))) from k = 1 to infinity

The two expressions are equivalent. I need help getting from the first expression to the second.

Your posts would be much easier to read if you would learn to use tex. I'm guessing you need the product to sum formulas:

http://www.sosmath.com/trig/prodform/prodform.html