Principle of Mathematical Induction

Principle of Mathematical Induction

Question

If tanA space equals space straight x space tanB comma show that fraction numerator sin left parenthesis straight A minus straight B right parenthesis over denominator sin left parenthesis straight A plus straight B right parenthesis end fraction space equals space fraction numerator straight x minus 1 over denominator straight x plus 1 end fraction.

Answer

                                    tanx = x tanB
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#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
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#6 {main}</pre>
rightwards double arrow                          space space space space tanA over tanB space equals space space straight x over 1       
Applying componendo/dividendo, we get
                       fraction numerator tanA minus tanB over denominator tanA plus tanB end fraction space equals space fraction numerator straight x minus 1 over denominator straight x plus 1 end fraction
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#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
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#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#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)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>
rightwards double arrow       space space fraction numerator sinA space cosB minus cosA space sinB over denominator sinA space cosB plus cosA space sinB end fraction space equals space fraction numerator straight x minus 1 over denominator straight x plus 1 end fraction
Hence,                   fraction numerator sin left parenthesis straight A minus straight B right parenthesis over denominator sin left parenthesis straight A plus straight B right parenthesis end fraction space equals fraction numerator straight x minus 1 over denominator straight x plus 1 end fraction

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