Prove trig identity: $(\sin \theta + 1)(\sin \theta − 1) = −\cos^2 θ$ This is my attempt: 
$(\sin \theta+1)(\sin \theta-1) = \sin\theta^2 - \sin\theta + \sin\theta - 1$
$= \sin^2\theta - 1$
$= -\cos^2\theta$
Is it correct, and can it be improved? Thanks!

Yes this is correct.You must be knowing that $(x+y)(x-y)=x^2-y^2$. Therefore $(sin\theta+1)(sin\theta-1)=sin^2\theta-1=-cos^2\theta$
