Principle of Mathematical Induction

Question

Find the values of other five trigonometric functions of the following:

$cosx space equals space minus 1 half comma space straight x$ lies in third quadrant

Answer

Here $space space cosx space equals space minus 1 half$
sinx<0, cosx<0, secx<0, cosecx<0, tanx>0, cotx>0 (∵ x lies in quadrant III)

Now, $sin squared straight x plus cos squared straight x space equals space 1$ $space space space rightwards double arrow space space space sin squared straight x plus 1 fourth equals 1 space space space space space space space space space space space rightwards double arrow space space space space space space space space space space sin squared straight x space equals space 3 over 4 space space space rightwards double arrow space space space sinx space equals space plus-or-minus fraction numerator square root of 3 over denominator 2 end fraction$

$rightwards double arrow$ $sinx space equals space minus fraction numerator square root of 3 over denominator 2 end fraction$ (∵ sinx is -ve)
$secx space equals space 1 over cosx space equals space minus 2$ , $cosecx space equals space 1 over sinx space equals space minus fraction numerator 2 over denominator square root of 3 end fraction comma$
$tanx space equals space sinx over cosx space equals space fraction numerator left parenthesis negative square root of 3 divided by 2 right parenthesis over denominator left parenthesis negative 1 divided by 2 right parenthesis end fraction space equals space square root of 3 comma$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$