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Trigonometric Functions

Short Answer Type

141.

Find the general solution of:

$sec squared 2 straight x space equals space 1 minus tan 2 straight x$

126 Views

142.

Find the general solution of:

$tan space 2 straight x space equals space tan space straight x$

104 Views

143.

Find the general solution of:

$cos space mx space plus space cos space nx space equals space 0$

114 Views

144. Find the general solution of the following trigonometric equation:

$square root of 3 space sinx space minus space cos space straight x space equals space square root of 2$

space space space space space square root of 3 space sin space straight x space minus space cos space straight x space equals space square root of 2

rightwards double arrow space space space space space space space square root of 3 space sin space straight x space minus space 1 space cosx space equals space square root of 2

Dividing throughout by

square root of left parenthesis square root of 3 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space 2 comma

we get

space space space space fraction numerator square root of 3 over denominator 2 end fraction sinx space minus space 1 half space cosx space equals space fraction numerator 1 over denominator square root of 2 end fraction

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space space space space space rightwards double arrow space space space space space space space space space space space space space space space sinx space cos straight pi over 6 space minus space cosx space sin straight pi over 6 space equals fraction numerator 1 over denominator square root of 2 end fraction

space space space rightwards double arrow space space sin open parentheses straight x minus straight pi over 6 close parentheses space equals space fraction numerator 1 over denominator square root of 2 end fraction space equals space sin space 45 degree space equals space sin straight pi over 4

rightwards double arrow

open parentheses straight x minus straight pi over 6 close parentheses space equals space nπ space plus space left parenthesis negative 1 right parenthesis to the power of straight n space straight pi over 4 comma space straight n space element of space straight Z

rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space straight x space equals space nπ space plus space left parenthesis negative 1 right parenthesis to the power of straight n space straight pi over 4 plus straight pi over 6 comma space straight n space element of space straight Z

which is the required general solution of the equation.

110 Views

145. Find the general solution of the following trigonometric equation:

tan space straight theta space plus space sec space straight theta space equals space square root of 3

122 Views

146. Find the general solution of the following trigonometric equation:

tan space straight x space plus space tan space 2 straight x space plus space tan space straight x space tan space 2 straight x space equals space 1

158 Views

147. Find the general solution of the following trigonometric equation:

tan squared straight theta space plus space cot squared straight theta space equals space 2

113 Views

148. Find the general solution of the equation:

cos space 3 straight x space equals space sin space 2 straight x.

96 Views

Long Answer Type

149.

Find the general solution of the equation:

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

117 Views

Short Answer Type

150.

Find the general solution of the equations:

$space space space tanx space plus space tan 2 straight x space plus space tan 3 straight x space equals space tanx space space tan 2 straight x space space tan 3 straight x$

104 Views