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prove the trig identity cos x 1 sinx cos x 1 sin x 2tan x

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Prove the trig identity: Cos x/1-sinx - Cos x/1+sin x = 2tan x

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Answer to a math question Prove the trig identity: Cos x/1-sinx - Cos x/1+sin x = 2tan x

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$=\frac{\sin(2x)}{(-\sin(x)+1)(\sin(x)+1)}$

$=\frac{\sin(2x)}{\cos^{2}(x)}$

$=2\tan(x)$

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