Answer:
x = 5π/6, 3π/2.
Step-by-step explanation:
cot^2 x- csc x - 1 = 0
cos^2 x / sin^2x - 1/ sin x - 1 = 0
(1 - sin^2x) / sin^2 x - 1 / sin x - 1 = 0
Multiply though by sin^2 x:
1 - sin^2x - sin x - sin^2 x = 0
2 sin^2 x + sin x - 1 = 0
(2 sinx - 1)( sin x + 1)
sin x = 1/2, -1.
when sin x = 1/2, x = π/6, 5π/6
when sin x = -1 , x = 3π/2.
