Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the general solution of the following trigonometric equation:

square root of 3 space sinx space minus space cos space straight x space equals space square root of 2

Answer
space space space space space square root of 3 space sin space straight x space minus space cos space straight x space equals space square root of 2            rightwards double arrow space space space space space space space square root of 3 space sin space straight x space minus space 1 space cosx space equals space square root of 2
Dividing throughout by
           square root of left parenthesis square root of 3 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space 2 comma we get
        space space space space fraction numerator square root of 3 over denominator 2 end fraction sinx space minus space 1 half space cosx space equals space fraction numerator 1 over denominator square root of 2 end fraction

<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>       space space space space space rightwards double arrow space space space space space space space space space space space space space space space sinx space cos straight pi over 6 space minus space cosx space sin straight pi over 6 space equals fraction numerator 1 over denominator square root of 2 end fraction
space space space rightwards double arrow space space sin open parentheses straight x minus straight pi over 6 close parentheses space equals space fraction numerator 1 over denominator square root of 2 end fraction space equals space sin space 45 degree space equals space sin straight pi over 4     rightwards double arrow     open parentheses straight x minus straight pi over 6 close parentheses space equals space nπ space plus space left parenthesis negative 1 right parenthesis to the power of straight n space straight pi over 4 comma space straight n space element of space straight Z

rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space straight x space equals space nπ space plus space left parenthesis negative 1 right parenthesis to the power of straight n space straight pi over 4 plus straight pi over 6 comma space straight n space element of space straight Z
which is the required general solution of the equation.


More Chapters from Principle of Mathematical Induction