Factor: csc^2x -2cotx-3

Question

Factor using trig identities

Answer 1

csc²x - 2cotx - 3 = 1 + cot²x - 2 cotx - 3 = cot²x - 2cotx - 2;

This is quadratic function for cotx. To factor it let solve quadratic equation: cot²x - 2cotx - 2 = 0,

cotx = 1 ± √3;. So, cot²x - 2cotx - 2 = (cotx - 1 - √3)(cotx - 1 + √3)