Question : What is the value of $\frac{1+\sin A}{\cos ^2 A}$?
Option 1: $\frac{1}{1-\sin A}$
Option 2: $\frac{1}{1+\sin A}$
Option 3: $\frac{1}{1+\cos A}$
Option 4: $\frac{1}{1-\cos A}$
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Correct Answer: $\frac{1}{1-\sin A}$
Solution :
$\frac{1+\sin A}{\cos ^2 A}$
= $\frac{1+\sin A}{1-\sin^2 A}$
= $\frac{1+\sin A}{(1-\sin A)(1+\sin A)}$
= $\frac{1}{1-\sin A}$
Hence, the correct answer is $\frac{1}{1-\sin A}$.
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