Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Prove the following:

fraction numerator sin 5 straight x plus sin 3 straight x over denominator cos 5 straight x plus cos 3 straight x end fraction space equals space tan 4 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>
Using C, D - FORMULA, we get
   L.H.S. = fraction numerator 2 sin open parentheses begin display style fraction numerator 5 straight x plus 3 straight x over denominator 2 end fraction end style close parentheses space cos open parentheses begin display style fraction numerator 5 straight x minus 3 straight x over denominator 2 end fraction end style close parentheses over denominator 2 cos open parentheses begin display style fraction numerator 5 straight x plus 3 straight x over denominator 2 end fraction end style close parentheses cos open parentheses begin display style fraction numerator 5 straight x minus 3 straight x over denominator 2 end fraction end style close parentheses end fraction space equals space fraction numerator 2 sin 4 straight x space cosx over denominator 2 cos 4 straight x space cosx end fraction equals space fraction numerator sin 4 straight x over denominator cos 4 straight x end fraction
            equals space tan 4 straight x space equals space straight R. straight H. straight S.
Hence, L.H.S. = R.H.S.

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