Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Prove that:

fraction numerator 1 plus sin 2 straight x minus cos 2 straight x over denominator 1 plus sin 2 straight x plus cos 2 straight x end fraction space equals space tanx

Answer

L.H.S. = fraction numerator 1 plus sin 2 straight x minus cos 2 straight x over denominator 1 plus sin 2 straight x plus cos 2 straight x end fraction space equals space fraction numerator left parenthesis 1 minus cos 2 straight x right parenthesis plus sin 2 straight x over denominator left parenthesis 1 plus cos 2 straight x right parenthesis plus sin 2 straight x end fraction
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          space space space equals space fraction numerator 2 sinx space left parenthesis sinx plus cosx right parenthesis over denominator 2 cosx space left parenthesis cosx plus sinx right parenthesis end fraction space equals space sinx over cosx space equals space tanx space equals space straight R. straight H. straight S.
Hence, L.H.S. = R.H.S.

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