Hello,
i am having some trouble figuring out this problem, any help would be great!
(cosx+sinx+1)(cosx+sinx-1)=sin2x
Hi there Aerowen, here's my take.
You need to expand out the brackets, the problem should fall out for you!
$\displaystyle (\cos x+\sin x+1)(\cos x+\sin x-1)$
$\displaystyle =\cos^2 x+\cos x \sin x-\cos x+\cos x \sin x+ \sin^2-\sin x + \cos x+\sin x-1$
Now grouping some like terms.
$\displaystyle =\cos^2 x+ \sin^2+\cos x \sin x+\cos x \sin x-\sin x +\sin x+ \cos x-\cos x-1$
Cancelling
$\displaystyle =\cos^2 x+ \sin^2+2\cos x \sin x-1$
Applying the pythagorean identity
$\displaystyle =1+2\cos x \sin x-1$
$\displaystyle =2\cos x \sin x$
$\displaystyle =2 \sin x\cos x$
$\displaystyle = \sin 2x$