# Solution for equation

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

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

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

robphy
Homework Helper
Gold Member
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:
danago
Gold Member
You can easily do it using the fact that:

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

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

robphy