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    Sin x = tan x

    Why can't you divide both sides by tan x to get:
    Cos x =1
    For which the solutions are 0 , 2pi etc
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    (Original post by TheAdviser101)
    Why can't you divide both sides by tan x to get:
    Cos x =1
    Because tan x might be equal to zero, and you always need to be sure that you are not dividing by zero.
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    (Original post by TheAdviser101)
    Sin x = tan x

    Why can't you divide both sides by tan x to get:
    Cos x =1
    For which the solutions are 0 , 2pi etc
    Because u lose a solution. You should always look to factorise when solving trig equations. for this question:
    - convert tanx into the identity sinx/cosx
    -sinx=sinx/cosx
    -multiply both sides by cosx to get rid of denominator
    -sinxcosx=sinx
    -take away sinx from both sides
    -sinxcosx-sinx=0
    -now take out the common factor of sinx
    -sinx (cosx-1)=0
    -so either sinx=0, or cosx-1=0

    As you mentioned, you get one of the solutions as being cosx=1 (cosx-1=0, cosx=1). However theres a second solution of sinx=0 which you would have missed had you not factorised. So just remember u should always look to factorise
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    (Original post by Tyson_Fury)
    Because u lose a solution. You should always look to factorise when solving trig equations. for this question:
    - convert tanx into the identity sinx/cosx
    -sinx=sinx/cosx
    -multiply both sides by cosx to get rid of denominator
    -sinxcosx=sinx
    -take away sinx from both sides
    -sinxcosx-sinx=0
    -now take out the common factor of sinx
    -sinx (cosx-1)=0
    -so either sinx=0, or cosx-1=0

    As you mentioned, you get one of the solutions as being cosx=1 (cosx-1=0, cosx=1). However theres a second solution of sinx=0 which you would have missed had you not factorised. So just remember u should always look to factorise
    Cheers mate 😀
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    (Original post by Pangol)
    Because tan x might be equal to zero, and you always need to be sure that you are not dividing by zero.
    So you never divide by cos, tan or sin because there is a chance they could be zero?
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    (Original post by TheAdviser101)
    Sin x = tan x

    Why can't you divide both sides by tan x to get:
    Cos x =1
    For which the solutions are 0 , 2pi etc
    It's not that you can't. The problem is that doing so could cause you to lose solutions.  \sin x = \tan x \Rightarrow \sin x = \frac{\sin x}{\cos x} \Rightarrow \frac{\sin x \cos x}{\sin x}=1 . Now you have to consider the cases where  \sin x = 0 which will occur every  m\pi|m\in\mathbb{Z} . So, you could potentially be dividing by 0.
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    (Original post by TheAdviser101)
    So you never divide by cos, tan or sin because there is a chance they could be zero?
    This would be a good rule to follow, unless there is something specific in the question that makes it clear that they will never be zero in this particular question.
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    (Original post by Pangol)
    This would be a good rule to follow, unless there is something specific in the question that makes it clear that they will never be zero in this particular question.
    I can't understand that part. How can a question tell you whether tan cos sin is not zero?
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    There are values of x, for which both sinx and tanx = 0 , so you can't divide by tan(x), since division by 0 is undefined, so write tanx as sinx/cosx.
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    (Original post by Naruke)
    It's not that you can't. The problem is that doing so could cause you to lose solutions.  \sin x = \tan x \Rightarrow \sin x = \frac{\sin x}{\cos x} \Rightarrow \frac{\sin x \cos x}{\sin x}=1 . Now you have to consider the cases where  \sin x = 0 which will occur every  m\pi|m\in\mathbb{Z} . So, you could potentially be dividing by 0.
    Thanks for the clear explanation
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    (Original post by TheAdviser101)
    I can't understand that part. How can a question tell you whether tan cos sin is not zero?
    This could happen if you are only told to consider particular values of x. For example, if your question had been to solve sin x = tan x for 0 < x < 180 (note the strict inequalities), you could divide by tan x becasue it is never zero for these values of x.
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    (Original post by Pangol)
    This could happen if you are only told to consider particular values of x. For example, if your question had been to solve sin x = tan x for 0 < x < 180 (note the strict inequalities), you could divide by tan x becasue it is never zero for these values of x.
    Ohhh that makes sense. I appreciate your help. Thanks .
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    (Original post by Tyson_Fury)
    Because u lose a solution. You should always look to factorise when solving trig equations. for this question:
    - convert tanx into the identity sinx/cosx
    -sinx=sinx/cosx
    -multiply both sides by cosx to get rid of denominator
    -sinxcosx=sinx
    -take away sinx from both sides
    -sinxcosx-sinx=0
    -now take out the common factor of sinx
    -sinx (cosx-1)=0
    -so either sinx=0, or cosx-1=0

    As you mentioned, you get one of the solutions as being cosx=1 (cosx-1=0, cosx=1). However theres a second solution of sinx=0 which you would have missed had you not factorised. So just remember u should always look to factorise
    advising the advisor, i like dat
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    (Original post by Tyson_Fury)
    Because u lose a solution. You should always look to factorise when solving trig equations. for this question:
    - convert tanx into the identity sinx/cosx
    -sinx=sinx/cosx
    -multiply both sides by cosx to get rid of denominator
    -sinxcosx=sinx
    -take away sinx from both sides
    -sinxcosx-sinx=0
    -now take out the common factor of sinx
    -sinx (cosx-1)=0
    -so either sinx=0, or cosx-1=0

    As you mentioned, you get one of the solutions as being cosx=1 (cosx-1=0, cosx=1). However theres a second solution of sinx=0 which you would have missed had you not factorised. So just remember u should always look to factorise
    So if there is no possible way to factorise e.g. 3sin x = cos x, You can cancel using identies right?
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    (Original post by TheAdviser101)
    So if there is no possible way to factorise e.g. 3sin x = cos x, You can cancel using identies right?
    Exactly what benjamin said above me 😊
 
 
 
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