If                 show that: from Mathematics Trigono
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    Trigonometric Functions

    Multiple Choice QuestionsShort Answer Type

    111.

    Prove the following:

    <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>

    121 Views
    Answer
    112.

    Prove the following:

    space space space fraction numerator sin space straight x minus sin space 3 straight x over denominator sin squared space straight x minus cos squared space straight x end fraction space equals space 2 space sin space straight x

    111 Views
    Answer
    113.

    Prove the following:

    fraction numerator cos space 4 straight x plus cos space 3 straight x plus cos space 2 straight x over denominator sin space 4 straight x plus sin space 3 straight x plus sin space 2 straight x end fraction equals space cot space 3 straight x

    114 Views
    Answer
    114.

    Prove that:

    <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>

    117 Views
    Answer
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    115.

    Show that:

    open parentheses cos space straight alpha space plus space cos space straight beta close parentheses squared space plus left parenthesis sin space straight alpha space plus space sin space straight beta right parenthesis squared space equals space 4 space cos squared space fraction numerator straight alpha minus straight beta over denominator 2 end fraction

    108 Views
    Answer
    116.

    If          sin space straight alpha space plus space sin space straight beta space equals space straight a

               space space cos space straight alpha space plus space cos space straight beta space equals space straight b comma

    show that:

    <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>

    124 Views
    Answer
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    117.

    If        sinα space plus space sinβ space equals space straight a
             space space cos space straight alpha space plus space cos space straight beta space equals space straight b comma

    show that:

    sin left parenthesis straight alpha plus straight beta right parenthesis space equals space fraction numerator 2 ab over denominator straight a squared plus straight b squared end fraction

    sin space straight alpha space plus space sin space straight beta space space equals space straight a space space space space space space space space space rightwards double arrow space space space space space space space space space space space 2 space sin open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses space equals space straight a          ...(i)

    cos space straight alpha space plus space cos space straight beta space equals space straight b space space space space space space space space space space rightwards double arrow space space space space space space 2 cos open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses space equals space straight b            ...(ii)

    Dividing (i) and (ii), we get

    fraction numerator 2 sin open parentheses begin display style fraction numerator straight alpha plus straight beta over denominator 2 end fraction end style close parentheses space cos open parentheses begin display style fraction numerator straight alpha minus straight beta over denominator 2 end fraction end style close parentheses over denominator 2 cos open parentheses begin display style fraction numerator straight alpha plus straight beta over denominator 2 end fraction end style close parentheses space cos open parentheses begin display style fraction numerator straight alpha minus straight beta over denominator 2 end fraction end style close parentheses end fraction space equals space straight a over straight b space space space space space space rightwards double arrow space space space space space space tan open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space equals space straight a over straight b

    sin left parenthesis straight alpha plus straight beta right parenthesis space equals space fraction numerator 2 space tan open parentheses begin display style fraction numerator straight alpha plus straight beta over denominator 2 end fraction end style close parentheses over denominator 1 plus tan squared open parentheses begin display style fraction numerator straight alpha plus straight beta over denominator 2 end fraction end style close parentheses end fraction                 open parentheses because space sin space 2 straight x space equals space fraction numerator 2 space tanx over denominator 1 plus tan squared straight x end fraction close parentheses

                   = fraction numerator 2 open parentheses begin display style straight a over straight b end style close parentheses over denominator 1 plus begin display style straight a squared over straight b squared end style end fraction space equals space fraction numerator 2 straight a over denominator straight b end fraction space cross times space fraction numerator straight b squared over denominator straight b squared plus straight a squared end fraction space equals space fraction numerator 2 ab over denominator straight a squared plus straight b squared end fraction

    Hence,     sin left parenthesis straight alpha plus straight beta right parenthesis space equals space fraction numerator 2 ab over denominator straight a squared plus straight b squared end fraction
    121 Views
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    118.

    Show that: sin space 51 degree space plus space cos space 81 degree space equals space cos space 21 degree

    120 Views
    Answer
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    119.

    Show that: 

    <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>

    124 Views
    Answer
    120.

    Show that:

    fraction numerator sin 11 straight x space sinx space plus space sin 7 straight x space sin 3 straight x over denominator cos 11 straight x space sinx space plus space cos space 7 straight x space sin 3 straight x end fraction = tan 8x

    107 Views
    Answer
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