Principle Of Mathematical Induction

Question
CBSEENMA11014302

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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