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Trigonometric Functions

Short Answer Type

61.

Prove the following:

$sin space left parenthesis straight n plus 1 right parenthesis straight x space sin left parenthesis straight n plus 2 right parenthesis straight x plus cos space left parenthesis straight n plus 1 right parenthesis straight x space cos left parenthesis straight n plus 2 right parenthesis straight x space equals space cosx$

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62.

Prove the following:

$space space space cos open parentheses straight pi over 4 minus straight x close parentheses space cos open parentheses straight pi over 4 minus straight y close parentheses minus sin open parentheses straight pi over 4 minus straight x close parentheses space sin open parentheses straight pi over 4 minus straight y close parentheses space equals space sin left parenthesis straight x plus straight y right parenthesis$

111 Views

Long Answer Type

63.

If $space space cot space straight alpha space equals space 1 half$ and $sec space straight beta space equals space minus 5 over 3$ where $straight pi less than straight alpha less than fraction numerator 3 straight pi over denominator 2 end fraction$ and $straight pi over 2 less than straight beta less than straight pi comma$ find the

value of $tan left parenthesis straight alpha plus straight beta right parenthesis.$ State the quadrant in which $space space left parenthesis straight alpha plus straight beta right parenthesis$ terminates.

158 Views

Short Answer Type

64.

Prove that:

$sin squared straight A minus sin squared straight B space equals space sin left parenthesis straight A plus straight B right parenthesis. space sin left parenthesis straight A minus straight B right parenthesis$

118 Views

65.

Prove that:

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

121 Views

66.

Prove that:

$cos squared straight A minus sin squared straight B space equals space cos left parenthesis straight A plus straight B right parenthesis. space cos left parenthesis straight A minus straight B right parenthesis$

114 Views

67.

Prove the following:

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

128 Views

68.

Prove the following:

$space space space space cos squared 2 straight x minus cos squared 6 straight x space equals space sin space 4 straight x space sin 8 straight x$

103 Views

69.
Show that: $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

Let $straight A space equals space straight pi over 8 plus straight x over 2 comma space space space space space straight B equals space straight pi over 8 minus straight x over 2$

L.H.S. = $cos squared open parentheses straight pi over 8 plus straight x over 2 close parentheses minus sin squared open parentheses straight pi over 8 minus straight x over 2 close parentheses space equals space cos squared straight A minus sin squared straight B space equals space cos left parenthesis straight A plus straight B right parenthesis. space cos left parenthesis straight A minus straight B right parenthesis$

$space space space space equals cos open square brackets open parentheses straight pi over 8 plus straight pi over 2 close parentheses plus open parentheses straight pi over 8 minus straight pi over 2 close parentheses close square brackets. space cos open square brackets open parentheses straight pi over 8 plus straight x over 2 close parentheses minus open parentheses straight pi over 8 minus straight x over 2 close parentheses close square brackets$

$equals cos open parentheses straight pi over 4 close parentheses. cosx space equals space fraction numerator 1 over denominator square root of 2 end fraction cosx space equals space straight R. straight H. straight S.$
∴ L.H.S. = R.H.S.

Hence, $cos squared open parentheses straight pi over 8 plus straight x over 2 close parentheses minus sin squared open parentheses straight pi over 8 minus straight x over 2 close parentheses space equals space fraction numerator 1 over denominator square root of 2 end fraction cosx$

100 Views

70.

Show that:

$fraction numerator cos 18 degree plus sin 18 degree over denominator cos 18 degree minus sin 18 degree end fraction space equals space cot space 27 degree.$

120 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

69. Show that: