Answer
$\cos 2x$
Work Step by Step
Re-arrange the given equation as:
$=\dfrac{-\sin x}{\csc x}+\dfrac{\cos x}{\sec x}$
$=\dfrac{-\sin x}{\csc x}+\dfrac{\cos x}{\sec x}$
$=\dfrac{-\sin x}{1/\sin x}+\dfrac{\cos x}{1/\cos x}$
$=-\sin^2 x+\cos^2 x$
$=\cos^2 x-\sin^2 x$
$=\cos 2x$
