Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Prove the following;

<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>

Answer

L.H.S. = space space space fraction numerator sin left parenthesis straight A minus straight B right parenthesis over denominator cosA space cosB end fraction plus fraction numerator sin left parenthesis straight B minus straight C right parenthesis over denominator cosB space cosC end fraction plus fraction numerator sin left parenthesis straight C minus straight A right parenthesis over denominator cosC space cosA end fraction
equals fraction numerator sinA space cosB minus cosA space sinB over denominator cosA space cosB end fraction plus fraction numerator sinB space cosC minus cosB space sinC over denominator cosB space cosC end fraction plus fraction numerator sinC space cosA minus cosC space sinA over denominator cosC space cosA end fraction
equals space fraction numerator sinA space cosB over denominator cosA space cosB end fraction minus fraction numerator cosA space sinB over denominator cosA space cosB end fraction plus fraction numerator sinB space cosC over denominator cosB space cosC end fraction minus fraction numerator cosB space sinC over denominator cosB space cosC end fraction plus fraction numerator sinC space cosA over denominator cosC space cosA end fraction minus fraction numerator cosC space sinA over denominator cosC space cosA end fraction
equals space tanA minus tanB plus tanB minus tanC plus tanC minus tanA space equals space 0 equals space straight R. straight H. straight S.

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