Question

Rewrite with only sin x and cos x. Sin2x-cos2x

Answer 1

$\bf \textit{Double Angle Identities} \\\\ sin(2\theta)=2sin(\theta)cos(\theta) \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ 2cos^2(\theta)-1 \end{cases}\\\\ -------------------------------\\\\ sin(2x)-cos(2x)\implies 2sin(x)cos(x)~~~~-~~~~2cos^2(x)-1 \\\\\\ \stackrel{common~factor}{2cos(x)}[sin(x)~~-~~cos(x)]-1$