Principle of Mathematical Induction

Principle of Mathematical Induction


In any quadrilateral ABCD, show that sin (A + B) + sin (C + D) = 0.


ABCD is a quadrilateral
rightwards double arrow            space space space straight A plus straight B plus straight C plus straight D space equals space 360 degree space equals space 2 straight pi
rightwards double arrow                    <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/ at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/ line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#1 /home/config_admin/public/ mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/ com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/ com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/ com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/ com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>
rightwards double arrow           sin left parenthesis straight A plus straight B right parenthesis space equals space sin left square bracket 2 straight pi space minus space left parenthesis straight C space plus straight D right parenthesis right square bracket
x is quadrant IV means sinx is -ve.
∴              sin (A + B) = sin[2straight pi - (C + D)] = - sin (C + D)
Hence, sin (A + B) + sin (C + D) = 0

More Chapters from Principle of Mathematical Induction