To simplify the expression (sinα - tanα) / (cosα - 1), we can first use the trigonometric identities:

Now, substitute these identities into the expression:

(sinα - sinα / cosα) / (cosα - 1)

Simplify the expression further:

(sinα * cosα - sinα) / (cosα - 1)

Using trigonometric identities again, we get:

sin(α - α) / (cosα - 1)
= 0 / (cosα - 1)
= 0

Therefore, the simplified form of the expression (sinα - tanα) / (cosα - 1) is 0.