If cosec A - cot A = 1/4, then the value of tan A is:

As , cosecA - cotA = \(\frac{1}{4}\)   ----(1)

then cosec A + cotA = 4      -----(2)

Subtract 1 from 2

2cotA = 4 - \(\frac{1}{4}\) = \(\frac{15}{4}\)

cotA = \(\frac{15}{8}\)

So , tanA = \(\frac{8}{15}\)