Question

Which of the following steps correctly proves the identity sin(x)-tan(x)/sin(x)·tan(x) = cos(x)-1/sin(x)?

A) Multiply both the numerator and the denominator by cos(x).

B) Use the identity tan(x) = sin(x)/cos(x) to simplify the expression.

C) Factor out sin(x) from the numerator and denominator.

D) Apply the Pythagorean identity sin²(x)+cos²(x)=1 to manipulate the expression.

Answer 1

The correct steps to prove the given identity are multiplying by cos(x), using the identity tan(x) = sin(x)/cos(x), and factoring out sin(x).

Step-by-step explanation:

The correct steps to prove the identity sin(x)-tan(x)/sin(x)·tan(x) = cos(x)-1/sin(x) are:

1. Multiply both the numerator and the denominator by cos(x).
2. Use the identity tan(x) = sin(x)/cos(x) to simplify the expression.
3. Factor out sin(x) from the numerator and denominator.

By following these steps, you will obtain the expression cos(x)-1/sin(x), which is equal to the left side of the identity.