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ત્રિકોણમિતીય વિધેયો

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ગણિત ધોરણ 11 સેમિસ્ટર 1

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ગણિત

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નીચેના વિધેયનું શૂન્ય શોધો :
bold tan bold space open parentheses bold 2 bold theta bold space bold plus bold space bold 1 close parentheses


tan વિધેયનાં શૂન્યોનો ગણ open curly brackets bold kπ bold space bold vertical line bold space bold k bold space bold element of bold space bold Z close curly brackets છે.

bold therefore bold space bold tan bold space open parentheses bold 2 bold theta bold space bold plus bold space bold 1 close parentheses bold space bold equals bold space bold 0 bold space bold left right double arrow bold space bold 2 bold theta bold space bold plus bold space bold 1 bold space bold equals bold space bold kπ bold. bold space bold k bold space bold element of bold space bold Z

bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold left right double arrow bold space bold theta bold space bold equals bold space fraction numerator bold kπ bold space bold minus bold space bold 1 over denominator bold 2 end fraction bold comma bold space bold k bold space bold element of bold space bold Z bold space


bold therefore bold space bold tan bold space open parentheses bold 2 bold theta bold space bold plus bold space bold 1 close parentheses bold space નાં શૂન્યોનો ગણ open curly brackets fraction numerator bold kπ bold space bold minus bold space bold 1 over denominator bold 2 end fraction bold space bold vertical line bold space bold k bold space bold element of bold space bold Z close curly brackets space છે.


નીચેના વિધેયનું શૂન્ય શોધો :
cot 3x


વિધેયનાં શૂન્યોનો ગણ open curly brackets open parentheses bold 2 bold k bold space bold plus bold space bold 1 close parentheses bold space bold pi over bold 2 bold space bold vertical line bold space bold k bold space bold element of bold space bold Z close curly brackets છે.

bold therefore bold space bold cot bold space bold 3 bold x bold space bold equals bold space bold 0 bold space bold left right double arrow bold space bold 3 bold x bold space bold equals bold space open parentheses bold 2 bold k bold space bold plus bold space bold 1 close parentheses bold space bold pi over bold 2 bold comma bold space bold k bold space bold element of bold space bold Z

bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold left right double arrow bold space bold x bold space bold equals bold space open parentheses bold 2 bold k bold space bold plus bold space bold 1 close parentheses bold space bold pi over bold 6 bold comma bold space bold k bold space bold element of bold space bold Z


cot 3x નાં શૂન્યોનો ગણ open curly brackets open parentheses bold 2 bold k bold space bold plus bold space bold 1 close parentheses bold space bold pi over bold 6 bold space bold vertical line bold space bold k bold space bold element of bold space bold Z close curly brackets છે.

નીચેના વિધેયનું શૂન્ય શોધો :
sin x + 1


bold sin bold space bold x bold space bold plus bold space bold 1 bold space bold equals bold space bold 0 bold space bold left right double arrow bold space bold sin bold space bold x bold space bold equals bold space bold minus bold 1


ત્રિકોણમિતીય બિંદુ bold P bold space open parentheses bold theta close parentheses bold space bold equals bold space bold B bold apostrophe bold space open parentheses bold 0 bold comma bold space bold minus bold 1 close parentheses

x ની શક્ય કિંમતો.... bold minus bold pi over bold 2 bold comma bold space fraction numerator bold 3 bold pi over denominator bold 2 end fraction bold comma bold space fraction numerator bold 7 bold pi over denominator bold 2 end fraction bold comma bold space fraction numerator bold 11 bold pi over denominator bold 2 end fraction bold comma bold space bold. bold. bold. bold. bold. bold.


bold therefore bold space bold x bold space bold equals bold space open parentheses bold 4 bold k bold space bold minus bold space bold 1 close parentheses bold space bold pi over bold 2 bold comma bold space bold k bold space bold element of bold space bold Z

sin x + 1 નાં શૂન્યોનો ગણ open curly brackets open parentheses bold 4 bold k bold space bold minus bold space bold 1 close parentheses bold space bold pi over bold 2 bold space bold vertical line bold space bold k bold space bold element of bold space bold Z bold space close curly brackets છે.

નીચેના વિધેયનું શૂન્ય શોધો :
cos (3x + 2)


cos વિધેયનાં શૂન્યોનો ગણ open curly brackets open parentheses bold 2 bold k bold plus bold space bold 1 close parentheses bold space bold pi over bold 2 bold space bold vertical line bold space bold k bold space bold element of bold space bold Z close curly brackets છે.

bold therefore bold space bold cos bold space open parentheses bold 3 bold x bold space bold plus bold space bold 2 close parentheses bold space bold equals bold space bold 0

bold left right double arrow bold space bold 3 bold x bold space bold plus bold space bold 2 bold space bold equals bold space open parentheses bold 2 bold k bold space bold plus bold space bold 1 close parentheses bold space bold pi over bold 2 bold comma bold space bold k bold space bold element of bold space bold Z

bold left right double arrow bold space bold 3 bold x bold space bold equals bold space open parentheses bold 2 bold k bold space bold plus bold space bold 1 close parentheses bold space bold pi over bold 2 bold space bold minus bold space bold 2 bold comma bold space bold k bold space bold element of bold space bold Z

bold left right double arrow bold space bold x bold space bold equals bold space open parentheses bold 2 bold k bold space bold plus bold space bold 1 close parentheses bold space bold pi over bold 6 bold space bold minus bold space bold 2 over bold 3 bold comma bold space bold k bold space bold element of bold space bold Z


cos (3x + 2) નાં શૂન્યોનો ગણ open curly brackets open parentheses bold 2 bold k bold space bold plus bold space bold 1 close parentheses bold space bold pi over bold 6 bold space bold minus bold space bold pi over bold 2 bold space bold vertical line bold thin space bold k bold space bold element of bold space bold Z close curly brackets છે.


નીચેના વિધેયનું શૂન્ય શોધો :
cos x - 1


bold cos bold space bold x bold space bold minus bold space bold 1 bold space bold equals bold space bold 0 bold space bold left right double arrow bold space bold cos bold space bold x bold space bold equals bold space bold 1


ત્રિકોણમિતીય બિંદુ bold P bold space open parentheses bold theta close parentheses bold space bold equals bold space bold italic A bold space bold left parenthesis bold 1 bold comma bold space bold 0 bold right parenthesis

x ની શક્ય કિંમતો.... bold 2 bold pi bold comma bold space bold 4 bold pi bold comma bold space bold 6 bold pi bold comma bold space bold. bold. bold. bold. bold. bold.


bold therefore bold space bold x bold space bold equals bold space bold 2 bold kπ bold comma bold space bold k bold space bold element of bold space bold Z

cos x - 1 નાં શૂન્યોનો ગણ open curly brackets bold 2 bold kπ bold space bold vertical line bold space bold k bold space bold element of bold space bold Z close curly brackets છે.