Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the value of:

space space tan open parentheses fraction numerator 11 straight pi over denominator 8 end fraction close parentheses

Answer
tan open parentheses fraction numerator 11 straight pi over denominator 8 end fraction close parentheses space equals space tan open parentheses 11 over 8 cross times 180 degree close parentheses space equals space tan open parentheses 11 cross times 22 1 half to the power of ring operator close parentheses space equals space tan open parentheses 247 1 half to the power of ring operator close parentheses space equals space tan open parentheses 270 degree minus 22 1 half to the power of ring operator close parentheses
                 equals space cot space 22 1 half to the power of ring operator                                                 [∵ space space tan left parenthesis 270 degree minus straight theta right parenthesis space equals space cot space straight theta]
                  equals fraction numerator 1 over denominator tan 22 begin display style 1 half end style to the power of ring operator end fraction space equals space fraction numerator 1 over denominator square root of 2 minus 1 end fraction                                    [From part (a)]
                   <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>
Hence,      tan open parentheses fraction numerator 11 straight pi over denominator 8 end fraction close parentheses space equals space square root of 2 minus 1

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