The distance between the points (sin , cos ) and (cos , – sin ) is

The distance between two points in a plane is given by the formula:

d = sqrt[(x2 - x1)² + (y2 - y1)²]

Here, the points are (sin, cos) and (cos, -sin). Let's substitute these values into the formula:

d = sqrt[(cos - sin)² + (-sin - cos)²]

This simplifies to:

d = sqrt[(cos - sin)² + (-2sin)²]

d = sqrt[(cos² - 2sin*cos + sin²) + 4sin²]

Since sin² + cos² = 1 (from the Pythagorean identity), this further simplifies to:

d = sqrt[1 + 4sin² - 2sin*cos]

This is the distance between the points (sin, cos) and (cos, -sin).