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Trigonometric Functions

Short Answer Type

101.

Find the value of:

$cos straight pi over 8$

109 Views

Long Answer Type

102.

Prove that:

$tan space straight A space plus space tan space left parenthesis 60 degree plus straight A right parenthesis minus tan space left parenthesis 60 degree minus straight A right parenthesis space equals space 3 space tan space 3 straight A.$

134 Views

Short Answer Type

103.

Show that:

$cos straight pi over 7. space cos fraction numerator 2 straight pi over denominator 7 end fraction. space cos fraction numerator 4 straight pi over denominator 7 end fraction space equals space minus 1 over 8$

131 Views

Long Answer Type

104.

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

$tanx space equals space minus 4 over 3 comma space straight x space is space in space quadrant space II$

135 Views

105.
Find $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ in the following:

$cosx space equals space minus 1 third comma space straight x$ is in quadrant III

cosx space equals space minus 1 third

(Given) x lies in quadrant III

rightwards double arrow

straight pi less than straight x less than fraction numerator 3 straight pi over denominator 2 end fraction

rightwards double arrow

straight pi over 2 less than straight x over 2 less than fraction numerator 3 straight pi over denominator 4 end fraction

∴

straight x over 2

lies in quadrant II.

therefore space space cos straight x over 2 space and space tan straight x over 2

are -ve, but

sin straight x over 2

is +ve

Now,

cos open parentheses straight x over 2 close parentheses space equals space minus square root of fraction numerator 1 plus cosx over denominator 2 end fraction end root space equals space minus square root of fraction numerator 1 minus begin display style 1 third end style over denominator 2 end fraction end root space rightwards double arrow space space

cos open parentheses straight x over 2 close parentheses space equals space minus square root of 1 third end root

sin open parentheses straight x over 2 close parentheses space equals space plus square root of fraction numerator 1 minus cosx over denominator 2 end fraction end root space equals space square root of fraction numerator 1 plus begin display style 1 third end style over denominator 2 end fraction end root

rightwards double arrow

sin open parentheses straight x over 2 close parentheses space equals space square root of 2 over 3 end root

tan open parentheses straight x over 2 close parentheses space equals space fraction numerator sin open parentheses begin display style straight x over 2 end style close parentheses over denominator cos open parentheses begin display style straight x over 2 end style close parentheses end fraction space equals space fraction numerator square root of begin display style 2 over 3 end style end root over denominator negative square root of begin display style 1 third end style end root end fraction

rightwards double arrow

tan open parentheses straight x over 2 close parentheses space equals space minus square root of 2

135 Views

Short Answer Type

106.

If $cosx space equals space 1 half open parentheses straight a plus 1 over straight a close parentheses comma$ show that: $cos 2 straight x space equals space 1 half open parentheses straight a squared plus 1 over straight a squared close parentheses$

108 Views

107.

If cos x = $1 half open parentheses straight a plus 1 over straight a close parentheses comma$ show that:

$cos 3 straight x space equals space 1 half open parentheses straight a cubed plus 1 over straight a cubed close parentheses$

127 Views

108.

Prove the following:

$fraction numerator sin 5 straight x plus sin 3 straight x over denominator cos 5 straight x plus cos 3 straight x end fraction space equals space tan 4 straight x$

123 Views

109.

Prove the following:

$fraction numerator sin space straight x minus sin space straight y over denominator cos space straight x plus cos space straight y end fraction space equals space tan open parentheses fraction numerator straight x minus straight y over denominator 2 end fraction close parentheses$

130 Views

110.

Prove the following:

$sin open parentheses fraction numerator 7 straight pi over denominator 12 end fraction close parentheses plus cos open parentheses fraction numerator 7 straight pi over denominator 12 end fraction close parentheses space equals space cos open parentheses straight pi over 4 close parentheses space equals fraction numerator 1 over denominator square root of 2 end fraction$

123 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

Long Answer Type

105. Find in the following: is in quadrant III

Short Answer Type