If 7 cos A = 6, then find the numerical value of (cosec A + cot A) / (cosec A - cot A).

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Given: 7 cos A = 6
=> cos A = 6/7

We need to find (cosec A + cot A) / (cosec A - cot A).

Recall the identity:
(cosec A + cot A) / (cosec A - cot A) = (1 + cos A) / (1 - cos A)

This identity can be derived as follows:
- cosec A = 1/sin A
- cot A = cos A / sin A

So,
(cosec A + cot A) = (1 + cos A) / sin A
(cosec A - cot A) = (1 - cos A) / sin A

Therefore,
(cosec A + cot A) / (cosec A - cot A) = [(1 + cos A) / sin A] / [(1 - cos A) / sin A] = (1 + cos A) / (1 - cos A)

Now substitute cos A = 6/7:

(1 + 6/7) / (1 - 6/7) = (13/7) / (1/7) = 13

Hence, the value is 13.

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