Answer
See the steps.
Work Step by Step
$RHS = \cot{x}-\tan{x} = \dfrac{\cos{x}}{\sin{x}} - \dfrac{\sin{x}}{\cos{x}} = \dfrac{\cos^2{x}-\sin^2{x}}{\sin{x}\cos{x}}$
$RHS =\dfrac{\cos{2x}}{0.5 \sin{2x}} = 2 \cot{2x} = LHS$
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