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Trigonometric Functions

Short Answer Type

111.

Prove the following:

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

121 Views

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

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

114.
Prove that:

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

L.H.S. = $cos 2 straight x space cos straight x over 2 space minus space cos 3 straight x space cos fraction numerator 9 straight x over denominator 2 end fraction space equals space cos 2 straight x space cos straight x over 2 minus cos fraction numerator 9 straight x over denominator 2 end fraction cos 3 straight x$

= $1 half open square brackets 2 cos 2 straight x space cos straight x over 2 minus space 2 cos fraction numerator 9 straight x over denominator 2 end fraction cos 3 straight x close square brackets$

= $space space 1 half open curly brackets cos open parentheses 2 straight x plus straight x over 2 close parentheses plus cos open parentheses 2 straight x minus straight x over 2 close parentheses close curly brackets minus open curly brackets cos open parentheses fraction numerator 9 straight x over denominator 2 end fraction plus 3 straight x close parentheses plus cos open parentheses fraction numerator 9 straight x over denominator 2 end fraction minus 3 straight x close parentheses close curly brackets$

= $1 half open square brackets cos fraction numerator 5 straight x over denominator 2 end fraction plus cos fraction numerator 3 straight x over denominator 2 end fraction minus cos fraction numerator 15 straight x over denominator 2 end fraction minus cos fraction numerator 3 straight x over denominator 2 end fraction close square brackets$

= $1 half open square brackets cos fraction numerator 5 straight x over denominator 2 end fraction minus cos fraction numerator 15 straight x over denominator 2 end fraction close square brackets$ = $space space minus 1 half open square brackets cos fraction numerator 15 straight x over denominator 2 end fraction minus cos fraction numerator 5 straight x over denominator 2 end fraction close square brackets$

$equals fraction numerator negative 1 over denominator 2 end fraction open square brackets negative 2 sin open parentheses fraction numerator begin display style fraction numerator 15 straight x over denominator 2 end fraction end style plus begin display style fraction numerator 5 straight x over denominator 2 end fraction end style over denominator 2 end fraction close parentheses sin open parentheses fraction numerator begin display style fraction numerator 15 straight x over denominator 2 end fraction end style minus begin display style fraction numerator 5 straight x over denominator 2 end fraction end style over denominator 2 end fraction close parentheses close square brackets$

= $sin 5 straight x space sin open parentheses fraction numerator 5 straight x over denominator 2 end fraction close parentheses space equals space straight R. straight H. straight S.$

Hence, L.H.S. = R.H.S.

117 Views

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

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:

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

124 Views

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:

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

121 Views

118.

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

120 Views

119.

Show that:

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

124 Views

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

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

114. Prove that: