Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the general solution of:

tan space 2 straight x space equals space tan space straight x






Answer
tan space 2 straight x space equals space tan space straight x space
rightwards double arrow       space space 2 straight x space equals space nπ space plus space straight x comma space space straight n space element of space straight Z

rightwards double arrow            space space straight x space equals space nπ comma space space straight n space element of space straight Z
Hence, the general solution of the equation is
             space space space space space space straight x space equals space nπ comma space space straight n space element of space straight Z
Alternative method:
tan space 2 straight x space equals space tan space straight x rightwards double arrow space fraction numerator sin space 2 straight x over denominator cos space 2 straight x end fraction space equals space fraction numerator sin space straight x over denominator cos space straight x end fraction
rightwards double arrow             space space space sin space 2 straight x space cos space straight x space equals space cos space 2 straight x space sinx
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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...')
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#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                sin left parenthesis 2 straight x minus straight x right parenthesis space equals space 0           [∵ sinA cosB - cosA sinB = sin (A - B)]
rightwards double arrow                      sin space straight x space equals space 0
Hence, the general solution of the equation is
                space space straight x space equals space nπ comma space space straight n space element of space straight Z

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