The result tan^-1x - tan^-1y = tan^-1(x - y / (1 + xy)) is true when the value of xy is ……….

The equation tan^-1x - tan^-1y = tan^-1((x - y) / (1 + xy)) holds true under specific conditions for the product xy.

Condition for Validity

This identity is valid when the product of x and y, denoted as xy, is less than 1. In other words:

• xy < 1: The equation is true.
• xy = 1: The equation may not hold as expected.
• xy > 1: The equation does not hold.

Why This Matters

Understanding this condition is crucial for solving problems involving inverse tangent functions. It helps ensure that the mathematical manipulations you perform are valid and lead to correct results.