# Math Help - Trigonometric Limit problem

1. ## Trigonometric Limit problem

I am taking a college level Calculus class that involves trignometry, but I haven't taken trig for over 10 years. Please help if you can.

I need to find the limit of the following equation (or a helpful explanation of how I can find it).

(x - tan 2x)/(sin 2x) as x approaches 0

2. $\lim_{x \to 0}\frac{x-\tan 2x}{\sin 2x}$

Taking x=0 gives $\frac{0}{0}$

So we have to simplify it.

$\lim_{x \to 0}\frac{x}{\sin 2x}-\frac{\tan 2x}{\sin 2x}$

$\lim_{x \to 0}\frac{1}{2}\cdot\frac{1}{\frac{\sin 2x}{2x}}-\frac{\frac{\sin 2x}{\cos 2x}}{\sin 2x}$

You should know that $\lim_{x\to 0} \frac{\sin x}{x} = 1$. Same goes for 2x, $\lim_{x\to 0} \frac{\sin 2x}{2x} = 1$.

$\lim_{x \to 0} \frac{1}{2}\cdot\frac{1}{1}-\frac{1}{\cos 2x}$

$\frac{1}{2} - 1 = -\frac{1}{2}$