Question

write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression. cos xcsc x choose the correct answer below. a. tan x b. sec x c. 1 d. sin x e. cot x f. -1

Explanation:

Step1: Substitute the reciprocal identity

Recall that \(\csc x=\frac{1}{\sin x}\). So, \(\cos x\csc x=\cos x\times\frac{1}{\sin x}\).

Step2: Use the cotangent identity

Since \(\cot x = \frac{\cos x}{\sin x}\), then \(\cos x\times\frac{1}{\sin x}=\cot x\).

Answer:

E. \(\cot x\)