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Trigonometric Functions

Short Answer Type

591.

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

97 Views

Long Answer Type

592.

In any triangle ABC, prove that

(i) $tan open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses space equals space fraction numerator straight a minus straight b over denominator straight a plus straight b end fraction cot straight C over 2$

(ii) $tan open parentheses fraction numerator straight B minus straight C over denominator 2 end fraction close parentheses space equals space fraction numerator straight b minus straight c over denominator straight b plus straight c end fraction cot straight A over 2$

(iii) $tan open parentheses fraction numerator straight C minus straight A over denominator 2 end fraction close parentheses space equals space fraction numerator straight c minus straight a over denominator straight c plus straight a end fraction cot straight B over 2$

95 Views

Short Answer Type

593. Deduce projection formula from sine formula

137 Views

594. Deduce projection formula from cosine formula.

95 Views

595. Deduce cosine formula from projection formula

92 Views

596. Deduce cosine formula from sine formula

112 Views

Long Answer Type

597.
Prove in any triangle ABC

(i) $sin straight A over 2 equals square root of fraction numerator left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis over denominator bc end fraction end root$ (ii) $sin straight B over 2 equals square root of fraction numerator left parenthesis straight s minus straight c right parenthesis left parenthesis straight s minus straight a right parenthesis over denominator ac end fraction end root$ (iii) $sin straight C over 2 equals square root of fraction numerator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis over denominator ab end fraction end root$

(i) We have
   $2 space sin squared straight A over 2 space equals space 1 minus cosA space equals space 1 minus open square brackets fraction numerator straight b squared plus straight c squared minus straight a squared over denominator 2 bc end fraction close square brackets$

$equals space fraction numerator 2 bc minus straight b squared minus straight c squared plus straight a squared over denominator 2 bc end fraction equals fraction numerator straight a squared minus left parenthesis straight b minus straight c right parenthesis squared over denominator 2 bc end fraction$

   $equals fraction numerator left parenthesis straight a minus straight b plus straight c right parenthesis space left parenthesis straight a plus straight b minus straight c right parenthesis over denominator 2 bc end fraction equals fraction numerator left parenthesis 2 straight s minus 2 straight b right parenthesis left parenthesis 2 straight s minus 2 straight c right parenthesis over denominator 2 bc end fraction$

$rightwards double arrow$    $sin squared straight A over 2 space equals space fraction numerator left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis over denominator bc end fraction$

or $sin straight A over 2 equals square root of fraction numerator left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis over denominator bc end fraction end root$

Similarly, we can prove that

(ii) $sin straight B over 2 equals square root of fraction numerator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight c right parenthesis over denominator ac end fraction end root$

(iii) $sin straight C over 2 equals square root of fraction numerator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis over denominator ab end fraction end root$

102 Views

598.

Prove in any triangle ABC

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

102 Views

599.

Prove that in any triangle ABC:

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

124 Views

Short Answer Type

600.

Prove that in any triangle ABC:

$sin space straight A space equals space 2 over bc square root of straight s left parenthesis straight s minus straight a right parenthesis space left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis end root$

96 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

Long Answer Type

597. Prove in any triangle ABC(i) (ii) (iii)

Short Answer Type