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1. The problem statement, all variables and given/known data

(1 + cosθ + isinθ) / (1 - cosθ - isinθ) = icotθ/2

The first step in the solutions shows:

(2cos^2θ/2 + i2sinθ/2cosθ/2) / (2sin^2θ/2 - i2sinθ/2cosθ/2)

2. Relevant equations

I can't get there.

3. The attempt at a solution

I tried multiplying by: (1 - cosθ + isinθ) / (1 - cosθ + isinθ), with no luck.

the top line of my attempt shows i2sinθ + i2sinθcosθ

because 1-cos^2θ=sin^2θ

my signs could be wrong but still. how does the θ become θ/2. this is doing my head in. maybe just sleep on it.

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# Complex Numbers - Complex Roots of Unity

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