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Trigonometric Identities

prove that t...

Question

prove that
$\frac{{tan} A (cosecA - 1)}{1 + sin A} = secA$

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Solution

$\frac{tan A (cosec A-1)}{1 + sin A} \frac{\frac{sin A}{cos A} (\frac{1}{sin A} + 1)}{1 + sin A} \frac{\frac{sin A}{cos A} (\frac{1 + sin A}{sin A})}{1 + sin A} \frac{1}{cos A} = sec A$

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\sqrt{\frac{1 + s i n A}{1 - s i n A}} = s e c A + t a n A

{(s e c A - t a n A)}^{2} = \frac{1 - s i n A}{1 + s i n A}

\frac{1 - s i n A}{1 + s i n A} = (s e c A - t a n A)^{2}

\frac{c o t^{2} A (s e c A - 1)}{1 + s i n A} = s e c^{2} A (\frac{1 - s i n A}{1 + s e c A})

secA - t a n A = \frac{cos A}{1 + sin A}

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