Question

1+sin A/1-sin A = cosecA+1/cosecA-1​

Answer 1

Question:-

Prove that :-

$\bf{\frac{1 + sin \: </u><u>A</u><u>}{1 - sin \: </u><u>A</u><u>} = \frac{cosec \: </u><u>A</u><u> \: + 1}{cosec \: </u><u>A</u><u> - 1} }$

Formula used :-

• sin A = 1/ cosec A

Solution:-

Firstly ,take left hand side →

$\implies \: \frac{1 + sin \: A}{1 - sin \: A} \\ \\ \bf{ \implies \frac{1 + \frac{1}{cosec \: A} }{1 - \frac{1}{cosec \: A} } } \\ \\ \implies \: \bf{ \frac{ \frac{cosec \: A+ 1}{cosec \: A} }{ \frac{cosec \: A - 1}{cosec \: A} } } \\ \\ \bf{ \red{ \implies \: \frac{cosec \: A + 1}{cosec \: A - 1} }}$

Left hand side = Right hand side

Hence proved.

Answer 2

Answer:

Solution:-

Firstly ,take left hand side →

\begin{gathered} \implies \: \frac{1 + sin \: A}{1 - sin \: A} \\ \\ \bf{ \implies \frac{1 + \frac{1}{cosec \: A} }{1 - \frac{1}{cosec \: A} } } \\ \\ \implies \: \bf{ \frac{ \frac{cosec \: A+ 1}{cosec \: A} }{ \frac{cosec \: A - 1}{cosec \: A} } } \\ \\ \bf{ \red{ \implies \: \frac{cosec \: A + 1}{cosec \: A - 1} }}\end{gathered}

⟹

1−sinA

1+sinA

⟹

1−

cosecA

1

1+

cosecA

1

⟹

cosecA

cosecA−1

cosecA

cosecA+1

⟹

cosecA−1

cosecA+1

Left hand side = Right hand side

Hence proved.