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    Maths-
    General
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    Question

    cot invisible function application A plus cot invisible function application B plus cot invisible function application C plus fraction numerator cos invisible function application left parenthesis A plus B plus C right parenthesis over denominator sin invisible function application A sin invisible function application B sin invisible function application C end fraction equals

    1. c o t invisible function application A c o t invisible function application B c o t invisible function application C
    2. tan space A tan space B tan space C
    3. cos invisible function application A cos invisible function application B cos invisible function application C
    4. sin invisible function application A sin invisible function application B sin invisible function application C

    The correct answer is: c o t invisible function application A c o t invisible function application B c o t invisible function application C

      Take straight A equals straight B equals straight C equals 60 squared
      rightwards double arrow square root of 3 plus fraction numerator negative 0 over denominator 3 square root of 3 end fraction equals fraction numerator 1 over denominator 3 square root of 3 end fraction
      text  verify option (1)  end text cot invisible function application A cot invisible function application B cot invisible function application C equals fraction numerator 1 over denominator square root of 3 end fraction fraction numerator 1 over denominator square root of 3 end fraction fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator 1 over denominator 3 square root of 3 end fraction

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      text  In a  end text straight triangle A B C comma tan invisible function application A plus tan invisible function application B plus tan invisible function application C equals 6 and tan invisible function application A tan invisible function application B equals 2 then the triangle A B C is

      text  In a  end text straight triangle A B C comma tan invisible function application A plus tan invisible function application B plus tan invisible function application C equals 6 and tan invisible function application A tan invisible function application B equals 2 then the triangle A B C is

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      text  If  end text tan invisible function application straight A equals 1 comma tan invisible function application straight B equals 2 comma tan invisible function application straight C equals 3 text  then  end text straight A plus straight B plus straight C equals

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      text  If  end text alpha plus beta plus gamma equals pi over 2 text  and  end text cot invisible function application alpha comma cot invisible function application beta comma cot invisible function application gamma text  are in  end text straight A stack P with _ below with _ below text  then  end text cot invisible function application alpha times cot invisible function application gamma equals

      text  If  end text alpha plus beta plus gamma equals pi over 2 text  and  end text cot invisible function application alpha comma cot invisible function application beta comma cot invisible function application gamma text  are in  end text straight A stack P with _ below with _ below text  then  end text cot invisible function application alpha times cot invisible function application gamma equals

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      if tan space alpha comma tan space beta are the roots of the equation, x squared plus p x plus q equals 0 left parenthesis p not equal to 0 right parenthesis then

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      cot space B equals 2 tan space left parenthesis A minus B right parenthesis not stretchy rightwards double arrow 2 tan space B plus cot space B equals

      cot space B equals 2 tan space left parenthesis A minus B right parenthesis not stretchy rightwards double arrow 2 tan space B plus cot space B equals

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      text  If  end text sin text end text B equals 1 fifth times sin space left parenthesis 2 A plus B right parenthesis text  then  end text fraction numerator tan begin display style text end text end style left parenthesis A plus B right parenthesis over denominator tan begin display style text end text end style A end fraction equals

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      text  If  end text sin text end text x plus sin space y equals 3 left parenthesis cos space y minus cos space x right parenthesis text  then  end text fraction numerator sin begin display style text end text end style 3 x over denominator sin begin display style text end text end style 3 y end fraction equals

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      cos squared space left parenthesis A minus B right parenthesis plus cos squared space B minus 2 cos space left parenthesis A minus B right parenthesis cos A cos space B equals

      cos squared space left parenthesis A minus B right parenthesis plus cos squared space B minus 2 cos space left parenthesis A minus B right parenthesis cos A cos space B equals

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      cos space alpha sin space left parenthesis beta minus gamma right parenthesis plus cos space beta sin space left parenthesis gamma minus alpha right parenthesis plus cos space gamma sin space left parenthesis alpha minus beta right parenthesis equals

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      text  If tan  end text straight alpha equals 1 half text  and  end text sin text end text straight beta equals fraction numerator 1 over denominator square root of straight pi end fraction text  where  end text 0 less than straight alpha subscript 4 straight beta less than straight pi over 2 text  then  end text 2 straight beta text  is equal to  end text

      text  If tan  end text straight alpha equals 1 half text  and  end text sin text end text straight beta equals fraction numerator 1 over denominator square root of straight pi end fraction text  where  end text 0 less than straight alpha subscript 4 straight beta less than straight pi over 2 text  then  end text 2 straight beta text  is equal to  end text

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      text  If  end text cos text end text straight A equals negative 3 over 5 comma sin space straight B equals 7 over 25 text  and  end text 90 to the power of ring operator less than straight A less than 180 to the power of ring operator comma 0 to the power of ring operator less than straight B less than 90 to the power of ring operator text  then  end text tan text end text left parenthesis straight A plus straight B right parenthesis equals

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      text  If  end text cos text end text alpha equals negative 12 over 13 comma cot space beta equals 24 over 7 comma 90 to the power of ring operator less than alpha less than 180 to the power of ring operator and 180 to the power of ring operator less than straight beta less than 270 to the power of ring operator then the quadrant in which alpha plus beta lies

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      text  If  end text tan text end text straight A equals 17 over 18 comma tan space straight B equals 1 over 35 text  then  end text cos text end text left parenthesis straight A plus straight B right parenthesis equals

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