Question

Please Help Me!!!!
Simplify: (sin Θ − cos Θ) − (sin Θ + cos Θ)2?
a. -sin^2Θ
b. -cos2Θ
c. 0
d. -2sin(Θ)cos(Θ)-cos(Θ)+sin(Θ)-1

Answer 1

$(\sin\theta -\cos\theta) - (\sin\theta+\cos\theta)^2 = \sin\theta-\cos\theta+\\-(\sin^2\theta+\cos^2\theta+2\sin\theta\cos\theta) = \sin\theta-\cos\theta-(1+2\sin\theta\cos\theta)=\\=\boxed{-2\sin\theta\cos\theta-\cos\theta+\sin\theta-1}$