Question

Simplify (sin theta - cos theta) - (sin theta + cos theta)^2

Answer 1

$\bf \begin{array}{llll} [sin(\theta )-cos(\theta )] &-& [sin(\theta )+cos(\theta )]^2\\\\ &&sin^2(\theta )+2sin(\theta )cos(\theta )+cos^2(\theta )\\\\ &&sin^2(\theta )+cos^2(\theta )+2sin(\theta )cos(\theta )\\\\ &&1+2cos(\theta )sin(\theta )\\\\ &&1+sin(2\theta ) \end{array} \\\\\\ sin(\theta )-cos(\theta )-[1+sin(2\theta )]\implies sin(\theta )-cos(\theta )-1-sin(2\theta )$

I don't see it simplifying further.