Question
Prove.
$\frac{1+\sin A}{1-\sin A}=\frac{c o \sec A+1}{c o \sin A-1}$
$\frac{1+\sin A}{1-\sin A}=\frac{c o \sec A+1}{c o \sin A-1}$
✓
Answer
$ LHS =\frac{1+\sin A}{1-\sin A} $
$RHS =\frac{\operatorname{cosec} A+1}{\operatorname{cosec} A-1}=\frac{\frac{1}{\sin A}+1}{\frac{1}{\sin A}-1} $
$=\frac{1+\sin A}{1-\sin A}$
$RHS =\frac{\operatorname{cosec} A+1}{\operatorname{cosec} A-1}=\frac{\frac{1}{\sin A}+1}{\frac{1}{\sin A}-1} $
$=\frac{1+\sin A}{1-\sin A}$
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