Final answer:
To rewrite cot(θ)sec(θ) as a single trigonometric function, we simplify the expression by using the reciprocal and quotient identities of trigonometric functions. cot(θ)sec(θ) simplifies to cos(θ)/sin(θ).
Step-by-step explanation:
To rewrite cot(θ)sec(θ) as a single trigonometric function, we need to simplify the expression. Let's start by rewriting cot(θ) as 1/tan(θ) and sec(θ) as 1/cos(θ).
Therefore, cot(θ)sec(θ) = (1/tan(θ))(1/cos(θ)).
Next, using the quotient identity for tangent, we can rewrite tan(θ) as sin(θ)/cos(θ).
Substituting this into our expression, we get (1/(sin(θ)/cos(θ)))(1/cos(θ)).
Simplifying further, we have cos(θ)/sin(θ) for cot(θ)sec(θ).