Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Trigonometric Functions

Short Answer Type

601. Deduce the sine formula from cosine formula.

93 Views

Long Answer Type

602. In any triangle ABC, prove that

straight a over sinA space equals space straight b over sinB space equals space fraction numerator straight c over denominator sin space straight C end fraction comma

i.e. sides of the triangle are proportional to the sines of the opposite angles.

103 Views

603. In any triangle ABC, prove that

cos space straight A space equals space fraction numerator straight b squared plus straight c squared minus straight a squared over denominator 2 bc end fraction comma space cos space straight B space equals space fraction numerator straight c squared plus straight a squared minus straight b squared over denominator 2 ac end fraction space and space cos space straight C space equals space fraction numerator straight a squared plus straight b squared minus straight c squared over denominator 2 ab end fraction

where a, b and c are as usual the sides of the triangle.

108 Views

604.

In any triangle ABC, prove that:

(i) a = b cos C + c cos B (ii) b = c cos A + a cos C (iii) c = a cos B + b cos A

118 Views

Short Answer Type

605.

Prove that in any triangle ABC.

$space space straight capital delta space equals space 1 half bc space sinA space equals space 1 half ac space sinB space equals space 1 half ab space sinC equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root$

98 Views

606.

In any triangle ABC, prove that

$space space space straight capital delta space equals space 1 half straight a squared fraction numerator sinB space sinC over denominator sinA end fraction equals 1 half straight b squared fraction numerator sinC space sinA over denominator sin space straight B end fraction space equals space 1 half straight c squared fraction numerator sinA space sinB over denominator sin space straight C end fraction$

101 Views

607.
Prove that:

$straight s left parenthesis straight s minus straight a right parenthesis space tan straight A over 2 equals straight capital delta$

L.H.S. = $straight s left parenthesis straight s minus straight a right parenthesis square root of fraction numerator left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis over denominator straight s left parenthesis straight s minus straight a right parenthesis end fraction end root equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root equals straight capital delta equals straight R. straight H. straight S.$

90 Views

Long Answer Type

608.

Prove that for any triangle ABC

$2 straight R space equals space fraction numerator straight a over denominator sin space straight A end fraction equals straight b over sinB equals fraction numerator straight c over denominator sin space straight C end fraction$

where R is the radius of the circumcircle.

89 Views

Short Answer Type

609.

Prove that in any triangle ABC

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