# Homework Help: Prove trigonometric equality: 1 - cosx = 2(sin^2)*(x/2)

1. Aug 11, 2014

### needingtoknow

1. The problem statement, all variables and given/known data

It seems like a pretty straightforward equality but I when I tried to google it doesn't seem like it is known at all. All the paths I have tried have been dead ends.

The question was initially:

Find the limit as x approaches 0 for the expression (1-cosx)/x^2

In the second step of the solution, the expression became (2(sin^2)*(x/2)) / x^2 and I didn't know how the numerator changed to that new expression.

2. Aug 11, 2014

### LCKurtz

Do you know the identity $\cos(2x)= \cos^2x - \sin^2x = 1-2\sin^2x$? Solve for $1-\cos(2x)$ in terms of $\sin^2x$ and replace $x$ by $\frac\theta 2$ and you will have the identity you are looking for.

Last edited: Aug 11, 2014
3. Aug 11, 2014

### needingtoknow

Thank you that was exactly what I needed!