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Introduction to Trigonometry

Short Answer Type

61. Express sin 84° + tan 59°, in terms of trigonometric ratio of angle between 0° and 45°.

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62. In ΔABC, write cos

fraction numerator straight B plus straight C over denominator 2 end fraction

in terms of angle A.

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63. Express tan A in terms of sin A.

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64. Without using trigonometric tables, evaluate:

fraction numerator 7 space cos space 70 degree over denominator 2 space sin space 20 degree end fraction plus 3 over 2 fraction numerator space cos 55 degree. cosec 35 degree over denominator tan space 5 degree. space tan 45 degree. space tan 85 degree. space tan 65 degree end fraction

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65. If sin θ = cos θ, then write the value of θ. 0°<θ<90°.

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66. Write the value of 3 cos 52°. cos 38° - 3 sin 52°. sin 38°.°°

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67. Write the simplest value of

sinθ over cosecθ plus cosθ over secθ.

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68.

In right ABC, right-angled at B. AB = 5 cm and ∠ACB = 30°. Determine the length of the sides BC and AC.

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

space fraction numerator tan space 65 degree over denominator cot space 25 degree end fraction space equals space fraction numerator tan left parenthesis 90 degree minus 25 degree right parenthesis over denominator cot space 25 degree end fraction space equals space fraction numerator cot space 25 degree over denominator cot space 25 degree end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket because space left parenthesis tan space left parenthesis 90 degree minus straight theta right parenthesis space equals space cot space straight theta right square bracket space space space space space space space space space space space space space space space space space space space space equals space 1.

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70. Evaluate:

<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 #56mkdir(): 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 56<br />#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>

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