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11. State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = 12/5 for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ= 4/3 for some angle 6.

(i) False, since $space tanA space equals space Perpendicular over Base$ and perpendicular may be longer than base.
(ii) True, since $<pre>uncaught exception: file_put_contents(/home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/web/../../../../../../formulas/35/96/ec5690fd6e7cbf9b256641ccf1bd.ini): failed to open stream: Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php at line #12file_put_contents(/home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/web/../../../../../../formulas/35/96/ec5690fd6e7cbf9b256641ccf1bd.ini): failed to open stream: Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php line 12 #0 [internal function]: _hx_error_handler(2, 'file_put_conten...', '/home/config_ad...', 12, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php(12): file_put_contents('/home/config_ad...', 'mml=<math xmlns...') #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(48): sys_io_File::saveContent('/home/config_ad...', 'mml=<math xmlns...') #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(112): com_wiris_util_sys_Store->write('mml=<math xmlns...') #4 /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...') #5 /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) #6 /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) #7 {main}</pre>$ and hypotenuse being the longest side may be times the base.
(iii) False, since cos A is the abbreviation used for the cosine of angle A.
(iv) False, since cot A is used as an abbreviation for 'the cotangent of the angle A'.
(v) False, since the hypotenuse is the longest side in a right triangle. As such the value of sin A is always less than 1 (or, in particular equal to 1).

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12. Evaluate:
sin 60° cos 30° + sin 30° cos 60°

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13. Evaluate:
2 tan² 45° + cos² 30° - sin² 60°

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14. Evaluate:

fraction numerator cos space 45 degree over denominator sec space 30 degree space plus space cosec space 30 degree end fraction.

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15. Choose the correct option and justify your choice:

<pre>uncaught exception: <b>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 #57mkdir(): Permission denied</b><br /><br />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 57<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 57, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(57): mkdir('/home/config_ad...', 511) #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>

(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°.

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16.

Choose the correct option and justify your choice:
$fraction numerator 1 minus tan squared 45 degree over denominator 1 plus tan squared 45 degree end fraction$

(A) tan 90° (B) 1 (C) sin 45° (D) 0.

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17.

Choose the correct option and justify your choice:
sin 2A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°

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18.

Choose the correct option and justify your choice:
$fraction numerator 2 tan 30 degree over denominator 1 minus tan squared 30 degree end fraction equals$
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°.

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19.

If $tan left parenthesis straight A plus straight B right parenthesis space equals square root of 3 space space and space tan left parenthesis straight A minus straight B right parenthesis space equals space fraction numerator 1 over denominator square root of 3 end fraction semicolon$ $0 degree less than straight A plus straight B less or equal than 90 degree semicolon space space space straight A greater than straight B.$ Find A and B.