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Question

Eliminate θ from the equations tan(nθ+α)tan(nθ+β)=x and cot(nθ+α)cot(nθ+β)=y

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Solution

cot(nθ+α)cot(nθ+β)=y
1tan(nθ+α)1tan(nθ+β)=y
tan(nθ+β)tan(nθ+α)tan(nθ+α)tan(nθ+β)=y
xy=tan(nθ+α)tan(nθ+β)
tan(nθ+α)(nθ+β)
=tan(nθ+α)tan(nθ+β)1+tan(nθ+α)tan(nθ+β)
=x1xy=xyyx
tan(α+β)=xyyx

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