Step-by-step explanation:
(csc θ − 1) / cot θ
Multiply top and bottom by the conjugate csc θ + 1.
(csc θ − 1) (csc θ + 1) / (cot θ (csc θ + 1))
Distribute.
(csc²θ − 1) / (cot θ (csc θ + 1))
Use Pythagorean identity.
cot²θ / (cot θ (csc θ + 1))
Divide.
cot θ / (csc θ + 1)
