Question

Demuestra la siguiente identidad trigonometrica

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Answer 1

$\dfrac{1+\sin\theta}{1-\sin\theta}-\dfrac{1-\sin\theta}{1+\sin\theta}\\=\dfrac{(1+\sin\theta)(1+\sin\theta)-(1-\sin\theta)(1-\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}\\=\dfrac{(1+\sin\theta)^2-(1-\sin\theta)^2}{1-\sin^2\theta}\\=\dfrac{1+\sin^2\theta+2\sin\theta-(1+\sin^2\theta-2\sin\theta)}{\cos^2\theta}\\=\dfrac{4\sin\theta}{\cos^2\theta}\\\\=4\dfrac{\sin\theta}{\cos\theta}\cdot\dfrac{1}{\cos\theta}\\\\=4\tan\theta\sec\theta$

Espero se entienda, saludos!