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Trigonometric Identities

Prove that: ...

Question

Prove that:
$\frac{1 + sin A}{1 - sin A} = \frac{csc A + 1}{csc A - 1}$

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Solution

$\frac{1 + sin A}{1 - sin A}$ $(a s sin θ = \frac{1}{c o s e c θ})$
$= \frac{1 + \frac{1}{c o s e c A}}{1 - \frac{1}{c o s e c A}}$
$= \frac{(\frac{c o s e c A + 1}{c o s e c A})}{(\frac{c o s e c A - 1}{c o s e c A})}$
$= \frac{c o s e c A + 1}{c o s e c A - 1}$
Hence proved.

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\sqrt{\frac{sin A + 1}{1 - sin A}} + \sqrt{\frac{1 - sin A}{sin A + 1}} = 2 sec A

Q. Prove that :

\frac{1}{csc A - cot A} - \frac{1}{sin A} = \frac{1}{sin A} - \frac{1}{csc A + cot A}

\sqrt{(\frac{1 - sin A}{1 + sin A})} = sec A - tan A .

Q. Prove that :

\sqrt{\frac{1 + sin A}{1 - sin A}} = (sec A + tan A)

(sec A - tan A)^{2} = \frac{1 - sin A}{1 + sin A}

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