Question

60 cosec A=61 then find cot A​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$60cosec(A) = 61 \\ \\ cosec(A) = \frac{61}{60}$

Identity

$cosec {}^{2} (A) - cot {}^{2} (A) = 1 \\ cot {}^{2} (A) = cosec {}^{2} (A) - 1 \\ cot (A) = \sqrt{cosec {}^{2} (A) - 1}$

$cot(A) = \sqrt{cosec {}^{2} (A) - 1} \\ \\ = \sqrt{( \frac{61}{60}) {}^{2} - 1} \\ \\ = \sqrt{ \frac{3721}{3600} - 1 } \\ \\ = \sqrt{ \frac{3721 - 3600}{3600} } \\ \\ = \sqrt{ \frac{121}{3600} } \\ \\ = \frac{11}{60}$