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Trigonometric Functions

Short Answer Type

311.

Show that:

$cos 5 straight A equals 16 cos to the power of 5 straight A minus 20 cos cubed straight A plus 5 cosA.$

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312.

Show that:

$fraction numerator sin 54 degree over denominator sin 18 degree end fraction minus fraction numerator cos 54 degree over denominator cos 18 degree end fraction equals 2.$

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313.

Show that: $sin straight A. sin left parenthesis 60 degree minus straight A right parenthesis sin left parenthesis 60 degree plus straight A right parenthesis equals 1 fourth sin 3 straight A$ and deduce that $sin 20 degree sin 40 degree sin 60 degree sin 80 degree equals 3 over 16.$

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314.

Show that: $cos open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 16 straight pi over denominator 15 end fraction close parentheses equals 1 over 16$

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315.

Show that: $tanθ. tan left parenthesis straight theta plus 60 degree right parenthesis plus tanθ tan left parenthesis straight theta minus 60 degree right parenthesis plus tan left parenthesis straight theta plus 60 degree right parenthesis tan left parenthesis straight theta minus 60 degree right parenthesis equals minus 3$

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316.

Evaluate:

$cos straight pi over 8$

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317.

Evaluate:

$cos fraction numerator 11 straight pi over denominator 8 end fraction.$

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318.
If $cosx equals negative 4 over 5 comma straight pi less than straight x less than fraction numerator 3 straight pi over denominator 2 end fraction comma$ find values of (a) $sin straight x over 2$ (b) $cos straight x over 2.$

Solution not provided.

(a) $fraction numerator 3 over denominator square root of 10 end fraction$ (b) $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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319.

Prove that:

$fraction numerator sinx over denominator 1 plus cosx end fraction equals tan open parentheses straight x over 2 close parentheses$

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320.

Prove that:

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

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

318. If find values of (a) (b)

318.
If $cosx equals negative 4 over 5 comma straight pi less than straight x less than fraction numerator 3 straight pi over denominator 2 end fraction comma$ find values of (a) $sin straight x over 2$ (b) $cos straight x over 2.$