Question

w 4.11 - verifying/simplifying
ntities
verify the identity.
(csc xcdotcos x=cot x)
to verify the identity, start with the n
(csc xcdotcos x=\frac{1}{sin x}cdotcos x)
(=cot x)

Explanation:

Step1: Apply a reciprocal identity

Reciprocal identity: \(\csc x=\frac{1}{\sin x}\), so \(\csc x\cdot\cos x=\frac{1}{\sin x}\cdot\cos x\)

Step2: Apply a quotient identity

Quotient identity: \(\cot x = \frac{\cos x}{\sin x}\), so \(\frac{1}{\sin x}\cdot\cos x=\frac{\cos x}{\sin x}=\cot x\)

Answer:

The identity \(\csc x\cdot\cos x=\cot x\) is verified.