Question

Find the number of positive integral solutions of the equation tan^-1x + cos^-1(y/√(1 + y²) = sin^-1(3/√10) or tan^-1x + cot^-1y = tan^-13.

Answer 1

As x, y are positive integers, x = 1, 2 and corresponding y = 2, 7.

Hence, solutions are (x, y) = (1,2), (2,7).