How can I to solve $ \cos x = 2x$? I would like to get an approx. solution to the equation: $ \cos x = 2x$, I don't need an exact solution just some approx. And I need a solution using elementary mathematics (without derivatives etc).

At small angles $\alpha ≈ sin\alpha$, so at the equation we can write $2 sin\alpha≈ cos \alpha$. From that $tan \alpha ≈ 1/2$. The solution to the last equation is less than a degree off the exact solution to the original equation.
