Find the general solution of the following equation:

cos 3x + cos x - cos 2x = 0

Solution

cos 3x + cos x - cos 2x = 0
$rightwards double arrow$ $2 space cos open parentheses fraction numerator 3 straight x plus straight x over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator 3 straight x minus straight x over denominator 2 end fraction close parentheses minus cos space 2 straight x space equals space 0$
$rightwards double arrow$ $2 space cos 2 straight x space cosx space minus space cos space 2 straight x space equals 0$
$rightwards double arrow$ $cos space 2 straight x space left parenthesis 2 space cosx space minus space 1 right parenthesis space equals space 0$
$rightwards double arrow$ either cos 2x = 0 or $cos space straight x space equals space 1 half$
$rightwards double arrow$ either $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ or $cos space straight x space equals space cos straight pi over 3$
$rightwards double arrow$ either $straight x space equals space left parenthesis 2 straight n plus 1 right parenthesis straight pi over 2 comma space straight n space element of space straight Z$ or $straight x space equals space 2 straight pi space plus-or-minus space straight pi over 3 comma space space straight n space element of space straight Z$
$rightwards double arrow$ x = $space space left parenthesis 2 straight n plus 1 right parenthesis space straight pi over 2$ or $straight x space equals space 2 straight pi plus-or-minus straight pi over 3 comma space straight n element of space straight Z$