Principle Of Mathematical Induction

Question
CBSEENMA11014305

Prove that:

space space tan 3 straight x space equals space fraction numerator 3 tanx minus tan 3 straight x over denominator 1 minus 3 space tan squared straight x end fraction




Solution

Consider   tan3x =  tan(x + 2x)
                         equals fraction numerator tanx plus tan 2 straight x over denominator 1 minus tanx. tan 2 straight x end fraction equals fraction numerator tanx plus begin display style fraction numerator 2 tanx over denominator 1 minus tan squared straight x end fraction end style over denominator 1 minus tanx open parentheses begin display style fraction numerator 2 tanx over denominator 1 minus tan squared straight x end fraction end style close parentheses end fraction
                         equals fraction numerator tanx left parenthesis 1 minus tan squared straight x right parenthesis plus 2 space tanx over denominator left parenthesis 1 minus tan squared straight x right parenthesis minus 2 space tan squared straight x end fraction equals fraction numerator tanx minus tan cubed straight x plus 2 space tanx over denominator 1 minus 3 space tan squared straight x end fraction
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#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
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#6 {main}</pre>
∴            tan space 3 straight x space equals space fraction numerator 3 space tanx minus tan cubed straight x over denominator 1 minus 3 tan squared straight x end fraction
   

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