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Trigonometric Functions

Short Answer Type

561.

Prove the following:

$tan space left parenthesis 2 straight pi plus straight x right parenthesis space equals space tanx$

118 Views

562.

Prove that $tan 2 straight x space equals space fraction numerator 2 tanx over denominator 1 minus tan squared straight x end fraction.$

100 Views

563.

Prove that:

$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

101 Views

564.

Prove that:

$cos 3 straight x space equals space 4 cos cubed straight x minus 3 cosx$

108 Views

565.

Prove that:

$space space tan 3 straight x space equals space fraction numerator 3 tanx minus tan 3 straight x over denominator 1 minus 3 space tan squared straight x end fraction$

100 Views

566.

Prove that $sin space 2 straight x space equals space 2 space sinx space cosx space equals space fraction numerator 2 space tanx over denominator 1 plus tan squared straight x end fraction.$

102 Views

Long Answer Type

567.

Prove that:

$cos 2 straight x space equals space cos squared straight x minus sin squared straight x space equals space 1 minus 2 sin squared straight x space equals space 2 cos squared straight x minus 1 space equals space fraction numerator 1 minus tan squared straight x over denominator 1 plus tan squared straight x end fraction.$

143 Views

Short Answer Type

568.
Prove that: $cosA. space cos open parentheses straight pi over 3 minus straight A close parentheses. space cos open parentheses straight pi over 3 plus straight A close parentheses space equals space 1 fourth cos 3 straight A.$

L.H.S. = $cosA. space cos open parentheses straight pi over 3 minus straight A close parentheses. space cos open parentheses straight pi over 3 plus straight A close parentheses$

$equals space cosA. space open square brackets cos squared open parentheses straight pi over 3 close parentheses minus sin squared straight A close square brackets$

$open square brackets because space cos space left parenthesis straight A plus straight B right parenthesis. space cos left parenthesis straight A minus straight B right parenthesis space equals space cos squared straight A minus sin squared straight B close square brackets$

   $equals space cosA open square brackets open parentheses 1 half close parentheses squared minus sin squared straight A close square brackets$    $space space space space open parentheses because space cos straight pi over 3 space equals space cos 60 degree space equals space 1 half close parentheses$

   $equals space cosA space open square brackets 1 fourth minus sin squared straight A close square brackets space equals space cosA over 4 open square brackets 1 minus 4 sin squared straight A close square brackets$

   $equals space cosA over 4 open square brackets 1 minus 4 left parenthesis 1 minus cos squared straight A right parenthesis close square brackets space equals space cosA over 4 open square brackets negative 3 plus 4 space cos squared straight A close square brackets$

$equals 1 fourth left square bracket 4 space cos cubed straight A space minus space 3 space cosA right square bracket space equals space 1 fourth space cos space 3 straight A space left parenthesis because space cos space 3 straight A space equals space 4 space cos cubed straight A space minus space 3 space cosA right parenthesis$

Hence, $cosA. space cos open parentheses straight pi over 3 minus straight A close parentheses. space cos open parentheses straight pi over 3 plus straight A close parentheses space equals space 1 fourth cos 3 straight A$

$cosA. space cos left parenthesis 60 degree minus straight A right parenthesis. space cos left parenthesis 60 degree plus straight A right parenthesis space equals space 1 fourth cos 3 straight A$

111 Views

569.

Prove that: $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

104 Views

570.

Prove that:

$space space cos open parentheses straight x over 2 close parentheses space equals space plus-or-minus square root of fraction numerator 1 plus cosx over denominator 2 end fraction end root$