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Trigonometric Functions

Short Answer Type

41.

Prove that:

$2 sin squared open parentheses fraction numerator 11 straight pi over denominator 6 end fraction close parentheses plus cosec squared open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses. cos squared open parentheses straight pi over 3 close parentheses space equals space 3 over 2$

101 Views

42.

Prove that :

$cot squared open parentheses straight pi over 6 close parentheses plus cosec open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses plus 3 tan squared open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses space equals space 6$

92 Views

43.

Prove that:

$2 sin squared open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses plus 2 cos squared open parentheses straight pi over 4 close parentheses plus 2 sec squared open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses space equals 10$

99 Views

Long Answer Type

44.

Prove that:

$fraction numerator sin left parenthesis 180 degree plus straight theta right parenthesis. space cos left parenthesis 90 degree plus straight theta right parenthesis space tan left parenthesis 270 degree minus straight theta right parenthesis space cot left parenthesis 360 degree minus straight theta right parenthesis over denominator sin left parenthesis 360 degree minus straight theta right parenthesis space cos left parenthesis 360 degree plus straight theta right parenthesis space cosec left parenthesis 0 degree minus straight theta right parenthesis space sin left parenthesis 270 degree plus straight theta right parenthesis end fraction equals 1$

145 Views

Short Answer Type

45.

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

132 Views

46.

Show that: $cos 24 degree plus cos 55 degree plus cos 125 degree plus cos 204 degree plus cos 300 degree space equals space 1 half$

95 Views

47.
Show that: $sin squared straight pi over 8 plus sin squared fraction numerator 3 straight pi over denominator 8 end fraction plus sin squared fraction numerator 5 straight pi over denominator 8 end fraction plus sin squared fraction numerator 7 straight pi over denominator 8 end fraction space equals space 2$

L.H.S. = $space space sin squared straight pi over 8 plus sin squared fraction numerator 3 straight pi over denominator 8 end fraction plus sin squared fraction numerator 5 straight pi over denominator 8 end fraction plus sin squared fraction numerator 7 straight pi over denominator 8 end fraction$

$equals space space sin squared straight pi over 8 plus sin squared fraction numerator 3 straight pi over denominator 8 end fraction plus sin squared open parentheses fraction numerator 4 straight pi over denominator 8 end fraction plus straight pi over 8 close parentheses plus sin squared open parentheses fraction numerator 4 straight pi over denominator 8 end fraction plus fraction numerator 3 straight pi over denominator 8 end fraction close parentheses$

= $space space sin squared straight pi over 8 plus sin squared fraction numerator 3 straight pi over denominator 8 end fraction plus sin squared open parentheses straight pi over 2 plus straight pi over 8 close parentheses plus sin squared open parentheses straight pi over 2 plus fraction numerator 3 straight pi over denominator 8 end fraction close parentheses$

= $sin squared straight pi over 8 plus sin squared fraction numerator 3 straight pi over denominator 8 end fraction plus cos squared straight pi over 8 plus cos squared fraction numerator 3 straight pi over denominator 8 end fraction$ $open square brackets because space space sin open parentheses straight pi over 2 plus straight x close parentheses equals cos space straight x close square brackets$

$equals space open square brackets sin squared straight pi over 8 plus cos squared straight pi over 8 close square brackets plus open square brackets sin squared fraction numerator 3 straight pi over denominator 8 end fraction plus cos squared fraction numerator 3 straight pi over denominator 8 end fraction close square brackets$

= 1 + 1 (∵ $sin squared straight x plus cos squared straight x space equals space 1$ )

= 2 = R.H.S.

Hence, $sin squared straight pi over 8 plus sin squared fraction numerator 3 straight pi over denominator 8 end fraction plus sin squared fraction numerator 5 straight pi over denominator 8 end fraction plus sin squared fraction numerator 7 straight pi over denominator 8 end fraction space equals space 2$

113 Views

48.

Solve for x, when $sec open parentheses straight pi over 2 plus straight A close parentheses plus xsinA space tan open parentheses straight pi over 2 plus straight A close parentheses space equals space cos open parentheses straight pi over 2 plus straight A close parentheses.$ Also, find the value of x, when $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$