35. Prove that :cosec A +1(sec A + tan A)cosec A-1

1.	35. Prove that :cosec A +1(sec A + tan A)cosec A-1
Answer» Step-by-step EXPLANATION: $\frac{cosec \: a+ 1}{cosec \: a - 1} = \frac{cosec \: a + 1}{cosec \: a - 1} \times \frac{cosec \: a + 1}{cosec \: a + 1}$ $= \frac{ {(cosec \: a + 1)}^{2} }{ {cosec }^{2} a - 1}$ $= \frac{ {(cosec \: a \: + 1)}^{2} }{ {cot}^{2} a}$ $= { (\frac{cosec \: a + 1}{cot \: a} )}^{2}$ $= { (\frac{cosec \: a}{cot \: a} + \frac{1}{cot \: a} )}^{2}$ $= { (\frac{ \frac{1}{sin \: a} }{ \frac{cos \: a}{sin \: a} } + tan \: a) }^{2}$ $= { (\frac{1}{cos \: a} + tan \: a)}^{2}$ $= {(sec \: a \: + \: tan \: a)}^{2}$

Answer»

Step-by-step EXPLANATION:

$\frac{cosec \: a+ 1}{cosec \: a - 1} = \frac{cosec \: a + 1}{cosec \: a - 1} \times \frac{cosec \: a + 1}{cosec \: a + 1}$