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## Homework Statement

Given that 1+2cosx+2cos2x+2cos3x + ....+2cosnx = sin(x+1/2)x cosec(x/2)

Prove that 1-2cosx+2cos2x-2cos3x+....+2cos8x = cos(17/2)x sec(x/2)

## Homework Equations

## The Attempt at a Solution

1+2cosx+2cos2x+2cos3x + ....+2cos8x = sin(8+1/2)x cosec(x/2)

4cosx+4cos3x+4cos5x... = ?

I don't know how to continue. Or is there another way?