Question

Prove that:

$space space cos open parentheses straight x over 2 close parentheses space equals space plus-or-minus square root of fraction numerator 1 plus cosx over denominator 2 end fraction end root$

Solution

We know that
$cos space 2 straight A space equals space 2 cos squared straight A minus 1$
Replacing A by $space space straight x over 2 comma$ we get
$cosx space equals space 2 cos squared open parentheses straight x over 2 close parentheses minus 1$ $rightwards double arrow$ $2 cos squared open parentheses straight x over 2 close parentheses space equals space 1 plus cosx$
$rightwards double arrow$ $<pre>uncaught exception: file_put_contents(/home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/web/../../../../../../formulas/c2/da/2ad0fb29d62545a5154a3e8a9651.ini): failed to open stream: Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php at line #12file_put_contents(/home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/web/../../../../../../formulas/c2/da/2ad0fb29d62545a5154a3e8a9651.ini): failed to open stream: Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php line 12 #0 [internal function]: _hx_error_handler(2, 'file_put_conten...', '/home/config_ad...', 12, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php(12): file_put_contents('/home/config_ad...', 'mml=<math xmlns...') #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(48): sys_io_File::saveContent('/home/config_ad...', 'mml=<math xmlns...') #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(112): com_wiris_util_sys_Store->write('mml=<math xmlns...') #4 /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...') #5 /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) #6 /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) #7 {main}</pre>$ $rightwards double arrow$ $cos open parentheses straight x over 2 close parentheses equals plus-or-minus square root of fraction numerator 1 plus cosx over denominator 2 end fraction end root$

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Principle Of Mathematical Induction

Prove that:

$space space cos open parentheses straight x over 2 close parentheses space equals space plus-or-minus square root of fraction numerator 1 plus cosx over denominator 2 end fraction end root$

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