Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Trigonometric Functions

Short Answer Type

571.
Prove that:

$sin open parentheses straight x over 2 close parentheses space equals space plus-or-minus square root of fraction numerator 1 minus cosx over denominator 2 end fraction end root$

We know that:
 $cos space 2 straight A space equals space 1 minus 2 sin squared straight A$

Replacing A by $space space straight x over 2 comma$ we get

$cosx space equals space 1 minus 2 sin squared open parentheses straight x over 2 close parentheses$ $rightwards double arrow$ $2 sin squared open parentheses straight x over 2 close parentheses space equals space 1 minus cosx$

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

103 Views

572.

Prove that:

$tan open parentheses straight x over 2 close parentheses equals plus-or-minus square root of fraction numerator 1 minus cosx over denominator 1 plus cosx end fraction end root.$

210 Views

573.

Prove that:

$2 space sinA space cosB space equals space sin left parenthesis straight A plus straight B right parenthesis space plus space sin left parenthesis straight A minus straight B right parenthesis$

101 Views

574.

Prove that:
2 cosA sinB = sin (A + B) - sin (A - B)

130 Views

575.

Prove that:
2 cosA cosB = cos (A + B) + cos (A - B)

113 Views

576.

Prove that:
-2 sinA sinB = cos (A + B) - cos (A - B)

218 Views

577.

Prove the following:

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

91 Views

578.

Prove the following:

$sin space straight C space minus space sin space straight D space equals space 2 cos fraction numerator straight C plus straight D over denominator 2 end fraction sin fraction numerator straight C minus straight D over denominator 2 end fraction$

100 Views

579.

Prove the following:

$space space cosC space plus space cosD space equals space 2 cos fraction numerator straight C plus straight D over denominator 2 end fraction cos fraction numerator straight C minus straight D over denominator 2 end fraction$

116 Views

580.

Prove the following:

$cosC space minus space cosD space equals space minus 2 sin fraction numerator straight C plus straight D over denominator 2 end fraction sin fraction numerator straight C minus straight D over denominator 2 end fraction$

90 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

571. Prove that:

571.
Prove that:

$sin open parentheses straight x over 2 close parentheses space equals space plus-or-minus square root of fraction numerator 1 minus cosx over denominator 2 end fraction end root$