Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the principal and general solutions of the following equation:

sec space straight x space equals space 2


Answer

                                      sec space straight x space equals space 2
rightwards double arrow                                  cosx space equals space 1 half is positive.
∴  x lies in quadrant I or quadrant IV.
∴                      space space space cos space straight x space equals space 1 half space equals space cos space 60 degree  or cos space left parenthesis 360 degree space minus space 60 degree right parenthesis space equals space cos space 60 degree space space or space space cos space 300 degree
                                      equals space cos open parentheses straight pi over 3 close parentheses space or space cos open parentheses fraction numerator 5 straight pi over denominator 3 end fraction close parentheses
∴  The principal solutions are:   <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>
Now,         space space space cos space straight x space equals space 1 half space equals space cos open parentheses straight pi over 3 close parentheses space rightwards double arrow space straight x space equals space 2 nπ plus-or-minus straight pi over 3 comma space space straight n element of straight Z

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