# Thread: simplifying using half angle identity

1. ## simplifying using double angle identity

I think I got this right, but may be missing some steps or may be wrong entirely. The idea is to use the double angle identity to simplify

$\displaystyle sin4x$

$\displaystyle = 2sin2xcos2x$
$\displaystyle = 2(2sinxcosx)(1-2sin^2x)$
$\displaystyle = 4sinxcosx(1-2sin^2x)$
$\displaystyle = 4sinxcosx-8sin^3xcosx$

Is this right?

2. Originally Posted by satis
I think I got this right, but may be missing some steps or may be wrong entirely. The idea is to use the half angle identity to simplify

$\displaystyle sin4x$

$\displaystyle = 2sin2xcos2x$
$\displaystyle = 2(2sinxcosx)(1-2sin^2x)$
$\displaystyle = 4sinxcosx(1-2sin^2x)$
$\displaystyle = 4sinxcosx-8sin^3xcosx$

Is this right?
not sure how you can really simplify just $\displaystyle \sin{4x}$

also, the half angle formula is:

$\displaystyle \sin\left({\frac{\theta}{2}}\right) = \pm\sqrt{\frac{1-\cos{\theta}}{2}}$

3. that would be my mistake. I meant simplifying using the double angle formula. My apologies. Let's see if I can alter the thread title...yup!