# Math Help - Stuck with an identity

1. ## Stuck with an identity

Hi
I am asked to tackle this one below
I dont want to multiply the cosx by the cos2x yet all other routes I hit a dead end.
Any help would be great

2. Originally Posted by 200001
Hi
I am asked to tackle this one below
I dont want to multiply the cosx by the cos2x yet all other routes I hit a dead end.
Any help would be great

$\cos x(\frac{\cos^2 x-\sin^2 x}{\cos x+\sin x})=\frac{1}{2}$

$\cos x (\frac{(\cos x+\sin x)(\cos x-\sin x)}{\cos x+\sin x})=\frac{1}{2}$

Some simplication ,

$2\cos ^2 x-1-2\cos x\sin x=0$

$
\cos 2x=\sin 2x
$

3. brilliant, thanks
I made the error of trying to keep cos2a in its 'nice form' in the numerator