Principle of Mathematical Induction

Principle of Mathematical Induction

Question

If A, B, C, D are the vertices of a cyclic quadrilateral, show that sin A + sin B - sin C - sin D = 0.

Answer

A, B, C, D are the vertices of a cyclic quadrilateral.
rightwards double arrow                            A + C = 180 degree space equals space straight pi
and                            straight B plus straight D space equals space 180 degree space equals space straight pi
∴             sin space straight A plus sin space straight B space minus space sinC space minus space sin space straight D
                                          equals space sin left parenthesis 180 degree minus straight C right parenthesis plus sin left parenthesis 180 degree minus straight D right parenthesis minus sinC minus sinD
                                          equals space sin left parenthesis straight pi minus straight C right parenthesis space plus space sin left parenthesis straight pi minus straight D right parenthesis minus sin space straight C space minus space sinD
                                          <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>
                                                            (∵ x is quadrant II means sinx is +ve)
Hence, sinA + sinB - sinC - SinD = 0
                                          

More Chapters from Principle of Mathematical Induction