TMUA Zetta Paper 1 · Question 7

Let $A(n)$ be the area of a regular polygon with $n$ sides, each of length 1, where $n\ge3$ . Find, in terms of $n$ , an expression for

\frac{A(n)}{A(n+1)}.

[Angles in degrees]

\frac{(n+1)\tan\left(90-\frac{180}{n+1}\right)}{n\tan\left(90-\frac{180}{n}\right)}

\frac{n\tan\left(90-\frac{180}{n}\right)}{(n+1)\tan\left(90-\frac{180}{n+1}\right)}

\frac{n\tan\left(180-\frac{360}{n}\right)}{(n+1)\tan\left(180-\frac{360}{n+1}\right)}

\frac{4n\tan\left(180-\frac{360}{4n}\right)}{(n+1)\tan\left(180-\frac{360}{n+1}\right)}

\frac{n\tan\left(\frac{180}{n}\right)}{(n+1)\tan\left(\frac{180}{n+1}\right)}

\frac{n\tan\left(180-\frac{360}{n}\right)}{n\tan\left(90-\frac{180}{n}\right)}

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