Question

Find the principal and general solutions of the following equation:

$sec space straight x space equals space 2$

Solution

$sec space straight x space equals space 2$
$rightwards double arrow$ $cosx space equals space 1 half$ 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: $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
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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Principle Of Mathematical Induction

Find the principal and general solutions of the following equation:

$sec space straight x space equals space 2$

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