How do you solve tan(x)=sin(2x)?

[princiebebe57]

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

 

[cristo]

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

 

[princiebebe57]

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

 

[robphy]

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.)

 

[danago]

You can easily do it using the fact that:

$$\begin{array}{l}<br /> \tan x \equiv \frac{{\sin x}}{{\cos x}} \\ <br /> \sin (2x) \equiv 2\sin x\cos x \\ <br /> \end{array}$$

 

[unscientific]

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

 

[robphy]

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)