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ગણિત ધોરણ 11 સેમિસ્ટર 1

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ગણિત

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સાબિત કરો કે, open parentheses bold 3 bold space bold cos bold space bold pi over bold 3 bold space bold sec bold space bold pi over bold 3 bold space bold minus bold space bold 4 bold space bold sin bold space bold pi over bold 6 bold space bold tan bold space bold pi over bold 4 close parentheses bold space bold italic c bold italic o bold italic s bold space bold 2 bold pi bold space bold equals bold space bold 1


open parentheses bold 3 bold space bold cos bold space bold pi over bold 3 bold space bold sec bold space bold pi over bold 3 bold space bold minus bold space bold 4 bold space bold sin bold space bold pi over bold 6 bold space bold tan bold space bold pi over bold 4 close parentheses bold space bold cos bold space bold 2 bold pi

bold equals bold space open parentheses bold 3 bold space bold cross times bold space bold 1 over bold 2 bold space bold cross times bold space bold 2 bold space bold minus bold space bold 4 bold space bold cross times bold space bold 1 over bold 2 bold space bold cross times bold space bold 1 close parentheses bold space open parentheses bold 1 close parentheses

bold equals bold space bold 3 bold space bold minus bold space bold 2

bold equals bold space bold 1

bold 2 bold space bold sin to the power of bold 2 bold space bold pi over bold 4 bold space bold plus bold space bold 2 bold space bold cos to the power of bold 2 bold space bold pi over bold 4 bold space bold plus bold space bold sec to the power of bold 2 bold space bold pi over bold 3 નું મૂલ્ય મેળવો.

bold 2 bold space bold sin to the power of bold 2 bold space bold pi over bold 4 bold space bold plus bold space bold 2 bold space bold cos to the power of bold 2 bold space bold pi over bold 4 bold space bold plus bold space bold sec to the power of bold 2 bold space bold pi over bold 3

bold equals bold space bold 2 bold space open parentheses fraction numerator bold 1 over denominator square root of bold 2 end fraction close parentheses to the power of bold 2 bold space bold plus bold space bold 2 bold space open parentheses fraction numerator bold 1 over denominator square root of bold 2 end fraction close parentheses to the power of bold 2 bold space bold plus bold space open parentheses bold 2 close parentheses to the power of bold 2

bold equals bold space bold 2 bold space bold cross times bold space bold 1 over bold 2 bold plus bold space bold 2 bold space bold cross times bold space bold 1 over bold 2 bold space bold plus bold space bold 4

bold equals bold space bold 1 bold space bold plus bold space bold 1 bold space bold plus bold space bold 4

bold equals bold space bold 6

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#2 [internal function]: _hx_lambda->execute('Http Error #404')
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(532): call_user_func_array(Array, Array)
#4 [internal function]: haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Http Error #404')
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#6 [internal function]: _hx_lambda->execute('Http Error #404')
#7 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(27): call_user_func_array(Array, Array)
#8 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Http Error #404')
#9 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), NULL, NULL)
#10 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(40): haxe_Http->request(true)
#11 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(80): com_wiris_plugin_impl_HttpImpl->request(true)
#12 /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)
#13 {main}</pre> નું મૂલ્ય મેળવો.

bold cot to the power of bold 2 bold space bold pi over bold 6 bold space bold plus bold space bold cosec bold space bold pi over bold 6 bold space bold plus bold space bold 3 bold space bold tan to the power of bold 2 bold space bold pi over bold 6

bold equals bold space open parentheses square root of bold 3 close parentheses to the power of bold 2 bold space bold plus bold space bold 2 bold space bold plus bold space bold 3 bold space bold times bold space open parentheses fraction numerator bold 1 over denominator square root of bold 3 end fraction close parentheses to the power of bold 2

bold equals bold space bold 3 bold space bold plus bold space bold 2 bold space bold plus bold space bold 3 bold space bold cross times bold space bold 1 over bold 3

bold equals bold space bold 3 bold space bold plus bold space bold 2 bold space bold plus bold space bold 1

bold equals bold space bold 6

bold sec bold space bold pi over bold 6 bold space bold tan bold space bold pi over bold 3 bold space bold plus bold space bold sin bold space bold pi over bold 4 bold space bold cosec bold space bold pi over bold 4 bold space bold plus bold space bold cos bold space bold pi over bold 6 bold space bold cot bold space bold pi over bold 3 નું મૂલ્ય મેળવો.

bold sec bold space bold pi over bold 6 bold space bold tan bold space bold pi over bold 3 bold space bold plus bold space bold sin bold space bold pi over bold 4 bold space bold cosec bold space bold pi over bold 4 bold space bold plus bold space bold cos bold space bold pi over bold 6 bold space bold cot bold space bold pi over bold 3

bold equals bold space fraction numerator bold 2 over denominator square root of bold 3 end fraction bold space bold times bold space square root of bold 3 bold space bold plus bold space fraction numerator bold 1 over denominator square root of bold 2 end fraction bold space bold times bold space square root of bold 2 bold space bold plus bold space fraction numerator square root of bold 3 over denominator bold 2 end fraction bold space bold times bold space fraction numerator bold 1 over denominator square root of bold 3 end fraction

bold equals bold space bold 2 bold space bold plus bold space bold 1 bold space bold 1 over bold 2

bold equals bold space bold 7 over bold 2

open parentheses bold sin bold space bold pi over bold 6 bold space bold plus bold space bold cos bold space bold pi over bold 6 close parentheses bold space open parentheses bold sin to the power of bold 2 bold space bold pi over bold 6 bold space bold minus bold space bold sin bold space bold pi over bold 6 bold space bold cos bold space bold pi over bold 6 bold space bold plus bold space bold cos to the power of bold 2 bold space bold pi over bold 6 close parentheses ની કિંમત શોધો.

open parentheses bold sin bold space bold pi over bold 6 bold space bold plus bold space bold cos bold space bold pi over bold 6 close parentheses bold space open parentheses bold sin to the power of bold 2 bold space bold pi over bold 6 bold space bold minus bold space bold sin bold space bold pi over bold 6 bold space bold cos bold space bold pi over bold 6 bold space bold plus bold space bold cos to the power of bold 2 bold space bold pi over bold 6 close parentheses

bold equals bold space open parentheses bold sin bold space bold pi over bold 6 close parentheses to the power of bold 3 bold space bold plus bold space open parentheses bold cos bold space bold pi over bold 6 close parentheses to the power of bold 3

bold equals bold space open parentheses bold 1 over bold 2 close parentheses to the power of bold 3 bold space bold plus bold space open parentheses fraction numerator square root of bold 3 over denominator bold 2 end fraction close parentheses to the power of bold 3

bold equals bold space bold 1 over bold 8 bold space bold plus bold space fraction numerator bold 3 square root of bold 3 over denominator bold 8 end fraction

bold equals bold space fraction numerator bold 1 bold space bold plus bold space bold 3 bold space square root of bold 3 over denominator bold 8 end fraction