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    I'm trying to do a question

    to solve 4sin x = 3 tan x

    so, I converted the tan x

    into 4sin x = 3sin x /cos x

    so I cross multiplied , for it to be 4sin x 3 Cos x = 3 sin x

    I subtratced 3 sin x


    Hence = 4sin x 3cos x - 3 sin x = 0

    can I factorise, if so, any tips or how would you do it?
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    4sinx = 3 tanx
    4sinx = 3sinx/cosx
    4sinx -3sinx/cosx = 0
    sinx(4-3/cosx) = 0
    so either sinx = 0
    or 4 = 3/cosx
    4cosx = 3
    cosx = 3/4

    I think this would be a correct way of doing it, I'm not very awake right now though.

    P.S: Be wary of just cancelling out sinx when trying to solve, as you will leave out solutions for sinx = 0
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    (Original post by KatheO11)
    I'm trying to do a question

    to solve 4sin x = 3 tan x

    so, I converted the tan x

    into 4sin x = 3sin x /cos x

    so I cross multiplied , for it to be 4sin x 3 Cos x = 3 sin x

    I subtratced 3 sin x


    Hence = 4sin x 3cos x - 3 sin x = 0

    can I factorise, if so, any tips or how would you do it?
    Your manipulation is off.

    4 \sin x = 3\tan x \Leftrightarrow 4 \sin x = \frac{3\sin x}{ \cos x} \Leftrightarrow 4 \sin x \cos x = 3 \sin x

    Then move sine over to the LHS and factor it out.
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    (Original post by Mosa99)
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    Dividing through by sin(x), in this case, removes some solutions. Instead, everything should be moved to one side, hence making the left-hand side equal to zero. After this the sin(x) should be factorised out and the equation can be solved normally from this point.
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    (Original post by KatheO11)
    into 4sin x = 3sin x /cos x

    so I cross multiplied , for it to be 4sin x 3 Cos x = 3 sin x
    The 3 belongs to the numerator so \cos x is alone.

    Think of this as 4 \sin x = \frac{3 \sin x}{\cos x} and simplify from there
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    (Original post by Mosa99)
    ..
    You should not cancel out the \sin x because that would reduce the number of solutions x has. Instead, move everything to one side and factorise it out and you'll have \sin x = 0 and that's one equation to solve for x.
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    What a silly mistake I did 😅 Thank you guys for correcting me!!
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    (Original post by Mosa99)
    What a silly mistake I did 😅 Thank you guys for correcting me!!
    Also it's advisable you don't post solutions in the future
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    (Original post by ManLike007)
    Also it's advisable you don't post solutions in the future
    Advice accepted professor!
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