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$f(x) = frac{1 – 2sin x}{2cos x}$
$f'(x) = frac{-2cos x cdot 2cos x – (1 – 2sin x)cdot (-2sin x)}{4cos^2 x} =$ $frac{-4cos^2 x + 2sin x – 4sin^2 x}{4cos^2 x} =$ $frac{-4 (cos^2 x + sin^2 x) + 2sin x}{4cos^2 x} =$ $frac{-4 + 2sin x}{4cos^2 x} =$ $frac{sin x – 2}{2cos^2 x}$
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