Answer
See the steps.
Work Step by Step
$RHS = \sec{x} \csc{x} -\cot{x} +tan{x} = \dfrac{1}{\sin{x}\cos{x}} -\dfrac{\sin{x}}{\cos{x}}+\dfrac{\cos{x}}{\sin{x}}$
$RHS =\dfrac{1}{\sin{x}\cos{x}} - \dfrac{\sin^2{x}-\cos^2{x}}{\cos{x} \sin{x}}$
$RHS =\dfrac{2}{\sin{2x}} - \dfrac{2\cos{2x}}{\sin{2x}} = \dfrac{2-2\cos{2x}}{\sin{2x}} = LHS$
