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Answer :
We know that , \( cos A \ = \ \frac{1}{sec A} \)
Now, \( sin^2A + cos^2A \ = \ 1 \)
=> \( sin^2A \ = \ 1 - cos^2A \)
=> \( sin A \ = \ \frac{ \sqrt{ sec^2A - 1}}{sec A} \)
\( tan^2A + 1 \ = \ sec^2A \)
=> \( tan A \ = \ \sqrt{sec^2A - 1} \)
\( cot A \ = \ \frac{1}{tan A} \)
=> \( cot A \ = \ \frac{1}{ \sqrt{sec^2A - 1}} \)
\( cosec A \ = \ \frac{1}{sin A} \)
=> \( cosec A \ = \ \frac{sec A}{ \sqrt{sec^2A - 1}} \)