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Trigonometric Functions

Short Answer Type

361.

Show that:

$space space open parentheses fraction numerator cosA plus cosB over denominator sinA minus sinB end fraction close parentheses to the power of straight n plus open parentheses fraction numerator sinA plus sinB over denominator cosA minus cosB end fraction close parentheses to the power of straight n space equals space open curly brackets table attributes columnalign left end attributes row cell 2 cot to the power of straight n open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses space space when space straight n space is space even end cell row cell space space space space space 0 space space space space space space space space space space space space space space space space when space straight n space is space odd end cell end table close$

$open square brackets Hint colon space straight L. straight H. straight S. equals cot to the power of straight n open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses open parentheses left parenthesis 1 right parenthesis to the power of straight n plus left parenthesis negative 1 right parenthesis to the power of straight n close parentheses close square brackets$

105 Views

Long Answer Type

362.

<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>

show that

(a)

tan open parentheses fraction numerator straight x plus straight y over denominator 2 end fraction close parentheses equals straight a over straight b

(b)

cos open parentheses fraction numerator straight x minus straight y over denominator 2 end fraction close parentheses space equals space fraction numerator square root of straight a squared plus straight b squared end root over denominator 2 end fraction.

110 Views

Short Answer Type

363.

Prove that:

$sinα plus sinβ plus sinγ minus sin left parenthesis straight alpha plus straight beta plus straight gamma right parenthesis space equals space 4 sin open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space sin open parentheses fraction numerator straight beta plus straight gamma over denominator 2 end fraction close parentheses space sin open parentheses fraction numerator straight gamma plus straight alpha over denominator 2 end fraction close parentheses$

109 Views

364.

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

138 Views

365.

space space space If space cos left parenthesis straight theta plus 2 straight alpha right parenthesis space equals space straight m space cosθ comma space show space that space cot space straight alpha space equals space fraction numerator 1 plus straight m over denominator 1 minus straight m end fraction tan left parenthesis straight alpha plus straight theta right parenthesis.

125 Views

366.

Show that:

$cos space 7 straight theta space plus space cos space 5 straight theta space plus space cos space 3 straight theta space plus space cos space straight theta space equals space 4 space cos space 4 straight theta space cos space 2 straight theta space cos space straight theta$

111 Views

367.

Show that: $sin space straight alpha space plus space sin space open parentheses straight alpha plus fraction numerator 2 straight pi over denominator 3 end fraction close parentheses plus sin space open parentheses straight alpha plus fraction numerator 4 straight pi over denominator 3 end fraction close parentheses equals 0.$

114 Views

368.

Show that:

If $fraction numerator siny over denominator sin left parenthesis 2 straight x plus straight y right parenthesis end fraction equals straight m over straight n comma$ show that $cot left parenthesis straight x plus straight y right parenthesis space equals space fraction numerator straight n minus straight m over denominator straight n plus straight m end fraction cotx.$

125 Views

369.
If $cosx space equals space 1 half open parentheses straight p plus 1 over straight p close parentheses comma$ show that:

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

Solution not provided.

120 Views

370.

If $cosx space equals space 1 half open parentheses straight p plus 1 over straight p close parentheses comma$ show that:

$space space space 2 space cos space 3 straight theta space equals space open parentheses straight p cubed plus 1 over straight p cubed close parentheses$

109 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

369. If show that: