Prove that $tan 2 straight x space equals space fraction numerator 2 tanx over denominator 1 minus tan squared straight x end fraction.$

Solution

We know that
$tan left parenthesis straight alpha plus straight beta right parenthesis space equals space fraction numerator tanα plus tanβ over denominator 1 minus tanα. tanβ end fraction$ ....(i)
Replacing $space space space space straight alpha space equals space straight beta space equals space straight x$ in (i), we get
$tan space 2 straight x space equals space fraction numerator tanx plus tanx over denominator 1 minus tanx. tanx end fraction equals fraction numerator 2 space tanx over denominator 1 minus tan squared straight x end fraction$
∴ $tan space 2 straight x space equals space fraction numerator 2 space tanx over denominator 1 minus tan squared straight x end fraction$

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Principle Of Mathematical Induction

Prove that $tan 2 straight x space equals space fraction numerator 2 tanx over denominator 1 minus tan squared straight x end fraction.$

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