Principle of Mathematical Induction

Prove the following: - Wired Faculty

Question

Prove the following:

$tan 4 straight x space equals space fraction numerator 4 tanx space left parenthesis 1 minus tan squared straight x right parenthesis over denominator 1 minus 6 tan squared straight x plus tan to the power of 4 straight x end fraction$

Solution

Using $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ we get
$tan 4 straight x space equals space fraction numerator 2 tan 2 straight x over denominator 1 minus tan squared 2 straight x end fraction space equals space fraction numerator 2. begin display style fraction numerator 2 space tanx over denominator 1 minus tan squared straight x end fraction end style over denominator 1 minus open parentheses begin display style fraction numerator 2 space tanx over denominator 1 minus tan squared straight x end fraction end style close parentheses squared end fraction$
$rightwards double arrow$ $tan 4 straight x space equals space fraction numerator begin display style fraction numerator 2. space 2 tanx over denominator 1 minus tan squared straight x end fraction end style over denominator begin display style fraction numerator left parenthesis 1 minus tan squared straight x right parenthesis squared minus 4 tan squared straight x over denominator left parenthesis 1 minus tan squared straight x right parenthesis squared end fraction end style end fraction space equals space fraction numerator 2.2 tanx over denominator 1 minus tan squared straight x end fraction cross times fraction numerator left parenthesis 1 minus tan squared straight x right parenthesis squared over denominator 1 plus tan to the power of 4 straight x minus 2 tan squared straight x minus 4 tan squared straight x end fraction$
Hence, $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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Principle Of Mathematical Induction

Prove the following:

$tan 4 straight x space equals space fraction numerator 4 tanx space left parenthesis 1 minus tan squared straight x right parenthesis over denominator 1 minus 6 tan squared straight x plus tan to the power of 4 straight x end fraction$

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