Question

plz explain how this step came

Answer 1

$\frac{(cos\theta-1)^2-sin^2\theta}{(sin\theta+cos\theta)^2-1^2}$Multiply them:
$= \frac{(sin\theta-cos\theta+1)(sin\theta+cos\theta+1)}{(sin\theta+cos\theta-1)(sin\theta+cos\theta+1)} = \frac{sin^2\theta-(cos^2\theta+1)}{(sin\theta+cos\theta)^2-1^2}$
This is achieved as we know that $x^{2} - y^{2} = (x+y)(x-y)$
also, we know that $sin^2\theta=cos^2\theta-1$
similarly, we have $cos^2+1=sin^2\theta$
Therefroe, by substituting these, we got the above answer