Principle of Mathematical Induction

Principle of Mathematical Induction

Question

In any triangle ABC, if <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)
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#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)
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#6 {main}</pre> show that angle straight A space equals space 60 degree

Answer
fraction numerator 1 over denominator straight c plus straight a end fraction plus fraction numerator 1 over denominator straight a plus straight b end fraction equals fraction numerator 3 over denominator straight a plus straight b plus straight c end fraction                                                         (Given)
  fraction numerator straight a plus straight b plus straight c plus straight a over denominator left parenthesis straight c plus straight a right parenthesis space left parenthesis straight a plus straight b right parenthesis end fraction space equals space fraction numerator 3 over denominator straight a plus straight b plus straight c end fraction

rightwards double arrow     space space left parenthesis 2 straight a plus straight b plus straight c right parenthesis space left parenthesis straight a plus straight b plus straight c right parenthesis space equals space 3 left parenthesis ac plus bc plus straight a squared plus ab right parenthesis
rightwards double arrow     2 straight a squared plus 2 ab plus 2 ac plus ab plus straight b squared plus bc plus ac plus bc plus straight c squared space equals space 3 ac plus 3 bc plus 3 straight a squared plus 3 ab

rightwards double arrow                     straight b squared plus straight c squared space equals space straight a squared plus bc
rightwards double arrow                straight b squared plus straight c squared minus straight a squared space equals space bc

rightwards double arrow                fraction numerator straight b squared plus straight c squared minus straight a squared over denominator bc end fraction space equals space 1
rightwards double arrow                  fraction numerator straight b squared plus straight c squared minus straight a squared over denominator 2 bc end fraction space equals space 1 half                        (Dividing each side by 2)

rightwards double arrow                             space space cos space straight A space equals space 1 half
Hence,                                angle straight A space equals space 60 degree


 

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