Principle Of Mathematical Induction

Question
CBSEENMA11013369

Prove the following:

space space space cos open parentheses straight pi over 4 minus straight x close parentheses space cos open parentheses straight pi over 4 minus straight y close parentheses minus sin open parentheses straight pi over 4 minus straight x close parentheses space sin open parentheses straight pi over 4 minus straight y close parentheses space equals space sin left parenthesis straight x plus straight y right parenthesis




Solution

Let open parentheses straight pi over 4 minus straight x close parentheses space equals space straight A and straight pi over 4 minus straight y space equals space straight B
                    L.H.S. = cos open parentheses straight pi over 4 minus straight x close parentheses space cos open parentheses straight pi over 4 minus straight y close parentheses minus sin open parentheses straight pi over 4 minus straight x close parentheses space sin open parentheses straight pi over 4 minus straight y close parentheses

                             equals space cosA space cosB space minus space sinA space sinB space equals space cos left parenthesis straight A plus straight B right parenthesis
                             equals cos open square brackets open parentheses straight pi over 4 minus straight x close parentheses plus open parentheses straight pi over 4 minus straight y close parentheses close square brackets space equals space cos open square brackets straight pi over 2 minus left parenthesis straight x plus straight y right parenthesis close square brackets
                              equals sin left parenthesis straight x plus straight y right parenthesis                    open square brackets because space cos open parentheses straight pi over 2 minus straight theta close parentheses space equals space sinθ close square brackets
                              = R.H.S.
∴                   L.H.S. = R.H.S
Hence,      <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>
                            

Sponsor Area