Question

establish the identity. csc θ · cos θ = cot θ
write the left side in terms of sine and cosine.
1/sin θ · cos θ
write the result from the previous step as a single fraction.
cos θ/sin θ (do not simplify.)
the fraction from the previous step then simplifies to cot θ using what?
a. cancellation property
b. quotient identity
c. even - odd identity
d. pythagorean identity
e. reciprocal identity

Explanation:

The quotient identity for cotangent is defined as $\cot\theta=\frac{\cos\theta}{\sin\theta}$. The left - hand side of the given identity, when rewritten in terms of sine and cosine and combined into a single fraction, results in $\frac{\cos\theta}{\sin\theta}$, which is equal to $\cot\theta$ by the quotient identity.

Answer:

B. Quotient Identity