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    Maths-
    General
    Easy

    Question

    text  If  end text cos text end text left parenthesis straight A minus straight B right parenthesis equals 3 divided by 5 text  and  end text tan space Atan space straight B equals 2 text end textthen which one of the following is true

    1. sin space left parenthesis A plus B right parenthesis equals 1 divided by 5
    2. sin space left parenthesis A plus B right parenthesis equals negative 1 divided by 5
    3. cos space left parenthesis A minus B right parenthesis equals 1 divided by 5
    4. cos space left parenthesis A plus B right parenthesis equals negative 1 divided by 5

    The correct answer is: cos space left parenthesis A plus B right parenthesis equals negative 1 divided by 5

      cos space A cos space B plus sin space A sin space B equals 3 divided by 5

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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

      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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      text  If  end text straight A comma straight B text  are acute angles,  end text sin space straight A equals 4 over 5 comma tan invisible function application straight B equals 5 over 12 text  then  end text sin text end text left parenthesis straight A plus straight B right parenthesis equals

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      text  If  end text sin text end text straight A equals fraction numerator 1 over denominator square root of 2 straight pi end root end fraction comma sin space straight B equals fraction numerator 1 over denominator square root of 5 end fraction comma 0 less than straight A comma straight B less than straight pi over 4 text  then  end text straight A plus straight B equals

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      text  If  end text tan text end text straight A equals fraction numerator sin begin display style space end style straight B over denominator 1 minus xcos space straight B end fraction text  and  end text tan text end text straight B equals fraction numerator ysin space straight A over denominator 1 minus ycos space straight A end fraction text  then  end text fraction numerator sin begin display style text end text end style straight A over denominator sin begin display style text end text end style straight B end fraction equals

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      text  If  end text straight A plus straight B plus straight C equals straight pi over 2 text  then  end text sum fraction numerator cos begin display style text end text end style left parenthesis straight B plus straight C right parenthesis over denominator cos begin display style text end text end style Bcos space straight C end fraction equals

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      text  In a  end text straight triangle ABC text  if  end text tan text end text straight B equals fraction numerator 2 sin space Asin space straight C over denominator sin begin display style space end style left parenthesis straight A plus straight C right parenthesis end fraction text  then  end text tan space straight A comma tan space straight B comma tan space straight C text  are in  end text

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