Write the other trigonometric ratios of A in terms of secA.

We know that , \( cos A \ = \ \frac{1}{sec A} \)

Now, \( sin^2A + cos^2A \ = \ 1 \)

=> \( sin^2A \ = \ 1 - cos^2A \)

=> \( sin A \ = \ \frac{ \sqrt{ sec^2A - 1}}{sec A} \)

\( tan^2A + 1 \ = \ sec^2A \)

=> \( tan A \ = \ \sqrt{sec^2A - 1} \)

\( cot A \ = \ \frac{1}{tan A} \)

=> \( cot A \ = \ \frac{1}{ \sqrt{sec^2A - 1}} \)

\( cosec A \ = \ \frac{1}{sin A} \)

=> \( cosec A \ = \ \frac{sec A}{ \sqrt{sec^2A - 1}} \)