Express the trigonometric ratios sin A, sec A, and tan A in terms of cot A.

Solution :

We know that   \(cosec^2 A\) = 1 + \(cot^2 A\)

\(\implies\)   \(1\over sin^2 A\) = 1 + \(cot^2 A\)   \(\implies\)  \(sin^2 A\) = \(1\over 1 + cot^2 A\)

\(\implies\)  sin A = \(1\over \sqrt{1 + cot^2 A}\)

Also,  we know that  \(sec^2 A\) = 1 + \(tan^2 A\)

\(\implies\)  \(sec^2 A\) = 1 + \(1\over cot^2 A\)

\(\implies\)  \(sec^2 A\) = \(cot^2 A + 1\over cot^2 A\)

\(\implies\)  sec A = \(\sqrt{cot^2 A + 1}\over cot A\)

Also, we know that, tan A = \(1\over cot A\)

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