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

61.

Prove the following:

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

122 Views

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.

   $cotα space equals space 1 half$

$rightwards double arrow$ $space space tanα space equals space 2$

$secβ space equals space minus 5 over 3$

We know that $space space sec squared straight beta space equals space 1 plus tan squared straight beta$

$rightwards double arrow$ $open parentheses fraction numerator negative 5 over denominator 3 end fraction close parentheses squared space equals space 1 plus tan squared straight beta$

$rightwards double arrow$    $tan squared straight beta space equals space 25 over 9 minus 1 space equals space 16 over 9$

$rightwards double arrow$ $tanβ space equals space minus 4 over 3$ [∵ $tanβ$ is -ve as $straight beta$ lies in IInd quadrant]

$rightwards double arrow$    $space space space space tan left parenthesis straight alpha plus straight beta right parenthesis space equals space fraction numerator tanα plus tanβ over denominator 1 minus tanα space tanβ end fraction space equals space fraction numerator 2 minus begin display style 4 over 3 end style over denominator 1 minus 2 open parentheses begin display style fraction numerator negative 4 over denominator 3 end fraction end style close parentheses end fraction space equals space fraction numerator begin display style fraction numerator 6 minus 4 over denominator 3 end fraction end style over denominator begin display style fraction numerator 3 plus 8 over denominator 3 end fraction end style end fraction equals space 2 over 11$

Now,    $straight pi less than straight alpha less than fraction numerator 3 straight pi over denominator 2 end fraction$ and $straight pi over 2 less than straight beta less than straight pi$

$rightwards double arrow$ $fraction numerator 3 straight pi over denominator 2 end fraction less than straight alpha plus straight beta less than fraction numerator 5 straight pi over denominator 2 end fraction$

We know that $tan left parenthesis straight alpha plus straight beta right parenthesis space is space plus ve$ in Ist and IIIrd quadrant.

∴ $straight alpha plus straight beta$ lies in 1st quadrant.

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

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

63. If and where and find the value of State the quadrant in which terminates.

Short Answer Type