Some Applications of Trigonometry

Evaluate without using trigonometric tables: - Wired Faculty

Question

Evaluate without using trigonometric tables:
$space space 2 open parentheses fraction numerator cos squared 20 degree plus cos squared 70 degree over denominator sin squared 25 degree plus sin squared 65 degree end fraction close parentheses minus tan space 45 degree plus space tan space 13 degree space tan space 23 degree space tan space 30 degree space tan space 67 degree space tan space 77 degree$

Solution

<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>

equals space 2 open square brackets fraction numerator sin space squared space 70 degree plus cos space squared 70 degree over denominator cos squared space 65 degree plus sin squared space 65 degree end fraction close square brackets minus 1 plus tan left parenthesis 90 degree minus 77 degree right parenthesis. space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space tan space 77 degree space. space tan space left parenthesis 90 degree minus 67 degree right parenthesis. space tan space space 67 degree space. space fraction numerator 1 over denominator square root of 3 end fraction

equals space 2 open parentheses 1 over 1 close parentheses minus 1 plus cot space 77 degree. space tan space 77 degree space. space cot space 67 degree space. space tan space 67 degree space fraction numerator 1 over denominator square root of 3 end fraction equals space 2 minus 1 plus 1.1. space fraction numerator 1 over denominator square root of 3 end fraction equals 2 minus 1 plus fraction numerator 1 over denominator square root of 3 end fraction equals space 1 plus fraction numerator 1 over denominator square root of 3 end fraction space equals space fraction numerator square root of 3 plus 1 over denominator square root of 3 end fraction

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