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Math Help - Trigno formula error

  1. #1
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    Trigno formula error

    Guys ,i justed wanted to ask out something
    if the formula given in NCERT is right
    Tan(A+B)=Tan A+Tan B/1-Tan A*Tan B
    then dont u think
    { Tan(A +B) }(1-Tan A*Tan B)= Tan A+Tan B
    should be right too
    but if put A & B =45
    then
    LHS=Not Defined(0)=Not Defined
    &
    RHS=1+1=2
    whats wrong in formula then
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by omega2692 View Post
    Guys ,i justed wanted to ask out something
    if the formula given in NCERT is right
    Tan(A+B)=Tan A+Tan B/1-Tan A*Tan B
    then dont u think
    { Tan(A +B) }(1-Tan A*Tan B)= Tan A+Tan B
    should be right too
    but if put A & B =45
    then
    LHS=Not Defined(0)=Not Defined
    &
    RHS=1+1=2
    whats wrong in formula then
    The formula is right

    But when A=B=45, tanA=1 and tanB=1
    Therefore, 1-tanA*tanB=0.

    But you cannot multiply both sides this way by 0
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by omega2692 View Post
    Guys ,i justed wanted to ask out something
    if the formula given in NCERT is right
    Tan(A+B)=Tan A+Tan B/1-Tan A*Tan B
    then dont u think
    { Tan(A +B) }(1-Tan A*Tan B)= Tan A+Tan B
    should be right too
    but if put A & B =45
    then
    LHS=Not Defined(0)=Not Defined
    &
    RHS=1+1=2
    whats wrong in formula then
    The formula is right, but you need to be careful about the domain of the expressions.

    For example:
    tan(A + B) = \frac{tan(A) + tan(B)}{1 - tan(A)~tan(B)}
    is clearly undefined for A = B = 45 as the denominator on the RHS is 0. Likewise the left hand side is undefined for A = B = 45, so no contradictions.

    The result is that when you solve this for tan(A) + tan(B):
    tan(A) + tan(B) = tan(A + B)~(1 - tan(A)~tan(B))
    and let A + B = 45, not only do you have an undefined quantity on the right hand side, but you have effectively multiplied both sides of the tan(A + B) equation by 0! So I wouldn't expect this equation to give any reasonable response for those values of A and B.

    -Dan
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