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Trigonometric Functions

Short Answer Type

91.

If $tan open parentheses straight x over 2 close parentheses space equals space 3 over 4 comma$ find the value of:

tan x.

107 Views

92.

Show that: $space space space square root of 2 plus square root of 2 plus 2 space cos space 4 straight theta end root end root space equals space 2 cosθ$

139 Views

93.

If space space tanx space equals space straight b over straight a comma

find the value of

straight a space cos space 2 straight x space plus space straight b space sin space 2 straight x.

119 Views

94.

Show that:

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

118 Views

95.

Show that:

$8 cos cubed open parentheses straight pi over 9 close parentheses minus 6 cos open parentheses straight pi over 9 close parentheses space equals space 1$

107 Views

96.

Show that:

$cos 4 straight A space equals space 1 minus 8 cos squared straight A space plus space 8 cos to the power of 4 straight A$

112 Views

97.
Show that:

$cos space 6 straight A space equals space 32 space cos to the power of 6 straight A space minus space 48 space cos to the power of 4 straight A space plus space 18 space cos squared straight A space minus 1$

Using $cos 2 straight x space equals space 2 space cos squared straight x minus 1$ and $cos 3 straight A space equals space 4 space cos cubed straight A space minus space 3 space cosA comma$ we get

$cos 6 straight A space equals space 2 cos squared 3 straight A space minus space 1$

   $equals space 2 left square bracket 4 space cos cubed straight A space minus space 3 space cosA right square bracket squared minus 1$

   $equals 2 left square bracket space 16 space cos to the power of 6 space straight A space plus space 9 space cos squared straight A space minus space 24 space cos to the power of 4 straight A right square bracket space minus space 1$

   $space space space space space equals 32 cos to the power of 6 straight A space minus space 48 cos to the power of 4 straight A space plus space 18 space cos squared straight A minus 1$

Hence, $cos space 6 straight A space equals space 32 space cos to the power of 6 straight A space minus space 48 space cos to the power of 4 straight A space plus space 18 space cos squared straight A space minus 1.$