Given: Cosec A = 13/12

To find: Value of tanA * cotA

Explanation:

We know that cosec A is the reciprocal of sin A. So, we can write:

cosec A = 1/sin A

Given that cosec A = 13/12, we can substitute this value in the above equation:

13/12 = 1/sin A

Cross-multiplying, we get:

sin A = 12/13

Now, we can use the Pythagorean identity to find the value of cos A. The Pythagorean identity states that:

sin^2 A + cos^2 A = 1

Substituting the value of sin A, we get:

(12/13)^2 + cos^2 A = 1

Simplifying, we have:

144/169 + cos^2 A = 1

cos^2 A = 1 - 144/169

cos^2 A = 25/169

Taking the square root of both sides, we get:

cos A = ± 5/13

Now, we have the values of sin A and cos A, so we can find the value of tan A using the formula:

tan A = sin A / cos A

Substituting the values, we get:

tan A = (12/13) / (± 5/13)

tan A = ± 12/5

Similarly, we can find the value of cot A using the formula:

cot A = 1 / tan A

Substituting the values, we get:

cot A = 1 / (± 12/5)

cot A = ± 5/12

Therefore, the value of tan A * cot A is:

(± 12/5) * (± 5/12)

The ± signs cancel out, so the value of tan A * cot A is:

12/5 * 5/12 = 1

Hence, the value of tan A * cot A is 1.