1. ## trigonometric identity problem

Hello,

i am having some trouble figuring out this problem, any help would be great!

(cosx+sinx+1)(cosx+sinx-1)=sin2x

2. Hi there Aerowen, here's my take.

You need to expand out the brackets, the problem should fall out for you!

$(\cos x+\sin x+1)(\cos x+\sin x-1)$

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

Now grouping some like terms.

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

Cancelling

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

Applying the pythagorean identity

$=1+2\cos x \sin x-1$

$=2\cos x \sin x$

$=2 \sin x\cos x$

$= \sin 2x$