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Question

if 2cosθ=x=1xand2cosϕ=y+1y etc., then prove that :
xyz....+1xyz....=2cos(θ+ϕ+....)

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Solution

From the given relations
x=cosθ+isinθ=eiθ
y=cosϕ+isinϕ=eiϕ
xyz....=ei(θ+ϕ+ψ+....)
1xyz....=ei(θ+ϕ+ψ+....)
xyz....+1xyz....2cos(θ+ϕ+ψ+....)

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