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Trigonometric Functions

Short Answer Type

531.

Prove the following:

$fraction numerator tan open parentheses begin display style straight pi over 4 end style plus straight x close parentheses over denominator tan open parentheses begin display style straight pi over 4 end style minus straight x close parentheses end fraction space equals space open parentheses fraction numerator 1 plus tanx over denominator 1 minus tanx end fraction close parentheses squared$

110 Views

532.

Prove the following:

$fraction numerator cos left parenthesis straight pi plus straight x right parenthesis space cos left parenthesis negative straight x right parenthesis over denominator sin space open parentheses straight pi minus straight x close parentheses space cos open parentheses begin display style straight pi over 2 end style plus straight x close parentheses end fraction equals space cot squared straight x$

103 Views

533.

Prove the following:

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

104 Views

534.

127 Views

535.

Find the general solution for the following equation:

$space space sin 2 straight x plus cosx space equals space 0$

117 Views

536.

Prove that:

$left parenthesis cosx plus cosy right parenthesis squared plus left parenthesis sinx minus siny right parenthesis squared equals 4 cos squared fraction numerator straight x plus straight y over denominator 2 end fraction$

118 Views

537.

Prove that:

$left parenthesis cosx minus cosy right parenthesis squared plus left parenthesis sinx minus siny right parenthesis squared space equals space 4 space sin squared fraction numerator straight x minus straight y over denominator 2 end fraction$

135 Views

538.

Prove that:

$sinx plus sin 3 straight x plus sin 5 straight x plus sin 7 straight x equals space 4 space cosx space cos 2 straight x space sin 4 straight x$

106 Views

539.

Prove that:

$sin 3 straight x plus sin 2 straight x minus sinx equals 4 sinx space cos straight x over 2 space cos fraction numerator 3 straight x over denominator 2 end fraction$

94 Views

540. Prove that the radian is a constant angle.

Proof: Draw a circle with centre at O and radius OA = r. Cut off an arc AB of length r. Join OA, OB and produce AO to meet the circle again in C.

Since the angles at the centre of a circle are proportional to the lengths of the arcs which subtend them.

∴ $fraction numerator angle AOB over denominator angle AOC end fraction space equals space fraction numerator arc space AB over denominator arc space ABC end fraction$