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How do you find the solution tan(x)=sin(2x)?

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- Thread starter princiebebe57
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- #1

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How do you find the solution tan(x)=sin(2x)?

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- #2

Staff Emeritus

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Can you express both sides in terms of sin(x) and cos(x)? That might be a good place to start.

- #3

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No...do i have to do that to find all the solution points?

- #4

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princiebebe57 said:No...do i have to do that to find all the solution points?

You could plot them and look for the intersection points.

But cristo's suggestion would probably yield more accurate ["closed form"] answers. (Be careful not to inadvertently throw away solutions.)

Last edited:

- #5

Gold Member

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[tex]

\begin{array}{l}

\tan x \equiv \frac{{\sin x}}{{\cos x}} \\

\sin (2x) \equiv 2\sin x\cos x \\

\end{array}

[/tex]

- #6

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square both sides...then make use of (a-b)^2 = (a+b)(a-b)

- #7

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unscientific said:square both sides...then make use of (a-b)^2 = (a+b)(a-b)

um...

(a-b)^2 = a^2 - 2ab + b^2

a^2 - b^2 = (a+b)(a-b)

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