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ત્રિકોણમિતિ

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ગણિત ધોરણ ૧૦

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ગણિત

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
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ત્રિકોણમિતિ
bold increment bold space bold ABC માં bold m bold space bold angle bold A bold space bold equals bold space bold 90 bold degree, જો bold AB bold space bold equals bold space bold 5 bold comma bold space bold AC bold space bold equals bold space bold 12 bold space અને bold BC bold space bold equals bold space bold 13 bold comma bold space તો bold sinC bold comma bold space bold cosC bold comma bold space bold tanB bold comma bold space bold cosB bold comma bold space bold sinB શોધો. 
Answer
    • bold increment bold space bold ABC માં bold m bold space bold angle bold B bold space bold equals bold space bold 90 bold degree bold comma bold space જો bold BC bold space bold equals bold space bold 3 bold space અને bold AC bold space bold equals bold space bold 5 bold comma bold spaceતો bold angle bold A ના બધા ત્રિકોણમિતીય ગુણોત્તરો શોધો. 
    Answer

    • જો bold cosA bold space bold equals bold space bold 4 over bold 5 bold commaતો bold siaA અને bold tanA શોધો. 

    Answer
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    જો bold cosecθ bold space bold equals bold space bold 13 over bold 5 bold comma તો bold tanθ અને bold cosθ શોધો. 



    bold increment bold space bold ABC માં bold m bold space bold angle bold B bold space bold equals bold space bold 90 bold degree

    ધારો કે bold m bold space bold angle bold ACB bold space bold equals bold space bold theta

    bold therefore bold cosecθ bold space bold equals bold space bold AC over bold AB bold space bold equals bold space bold 13 over bold 5 bold therefore bold space bold AC over bold 13 bold space bold equals bold space bold AB over bold 5 bold space bold equals bold space bold K bold space bold therefore bold space bold AC bold space bold equals bold space bold 13 bold K bold comma bold space bold AB bold space bold equals bold space bold 5 bold K bold space

    હવે, bold AB to the power of bold 2 bold space bold plus bold space bold BC to the power of bold 2 bold space bold equals bold space bold left parenthesis bold 13 bold K bold right parenthesis to the power of bold 2 bold space

    bold therefore bold space bold left parenthesis bold 5 bold K bold right parenthesis to the power of bold 2 bold space bold plus bold space bold BC to the power of bold 2 bold space bold equals bold space bold left parenthesis bold 13 bold K bold right parenthesis to the power of bold 2 bold space bold therefore bold space bold 25 bold K to the power of bold 2 bold space bold plus bold space bold BC to the power of bold 2 bold space bold equals bold space bold left parenthesis bold 13 bold K bold right parenthesis to the power of bold 2 bold space bold therefore bold space bold BC to the power of bold 2 bold space bold equals bold space bold 169 bold K to the power of bold 2 bold space bold minus bold space bold 25 bold K to the power of bold 2 bold space bold therefore bold space bold BC to the power of bold 2 bold space bold equals bold space bold 144 bold K to the power of bold 2 bold therefore bold space bold BC bold space bold equals bold space bold 12 bold K bold space bold tanθ bold space bold equals bold space bold AB over bold BC bold space bold equals bold space fraction numerator bold 5 bold K over denominator bold 12 bold K end fraction bold space bold equals bold space bold 5 over bold 12 bold cosθ bold space bold equals bold space bold BC over bold AC bold space bold equals bold space fraction numerator bold 12 bold K over denominator bold 13 bold KK end fraction bold space bold equals bold space bold 12 over bold 13 bold space 
    Answer
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    જો bold cosB bold space bold equals bold space bold 1 over bold 3 bold comma bold space તો બાકીના પાંચ ત્રિકોણમિતીય ગુણોત્તર શોધો.
    Answer
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