Simplifying using the Tangent Difference identity: \frac{2nr}{\tan(\frac{(n-2)\pi}{2n}})

omdw1u

omdw1u

Answered question

2022-02-27

Simplifying using the Tangent Difference identity:
2nrtan((n2)π2n}

Answer & Explanation

Lillie-May Sutton

Lillie-May Sutton

Beginner2022-02-28Added 3 answers

First, as you note:
tan((n2)π2n)=tan(π2πn)=tan(πnπ2)
Now remember that sin(aπ2)=cos(a) and cos(aπ2)=sin(a). So:
tan((n2)π2n=tan(πnπ2)
=sin(πnπ2)cos(πnπ2)
=cosπnsinπn
=cotπn
Therefore,
2nrtan((n2)π2n)=2nrcotπn=2nrtanπn.

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