Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Prove the following:

space space space fraction numerator sin space straight x minus sin space 3 straight x over denominator sin squared space straight x minus cos squared space straight x end fraction space equals space 2 space sin space straight x

Answer

L.H.S. = <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#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)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#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>
          equals fraction numerator 2 cos open parentheses begin display style fraction numerator 3 straight x plus straight x over denominator 2 end fraction end style close parentheses sin open parentheses begin display style fraction numerator 3 straight x minus straight x over denominator 2 end fraction end style close parentheses over denominator cos 2 straight x end fraction                 (∵ space space space cos space 2 straight x space equals space space cos squared space straight x space minus space sin squared space straight x)
                
           equals fraction numerator 2 cos 2 straight x space sinx over denominator cos space 2 straight x end fraction space equals space 2 sin space straight x space equals space straight R. straight H. straight S.
Hence,         L.H.S. = R.H.S.

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