Question

Considering only the values of θθ for which the expression is defined, which of the following is equivalent to the expression below?

tan⁡(−0)×sec⁡(−0)×cot⁡(0)
a) sec⁡(θ)
b) 1/sec⁡(θ)
c) 1/sec⁡(θ)−sec⁡(θ)
d) sec⁡(θ)−1

Answer 1

The expression tan(-θ) × sec(-θ) × cot(0) is equivalent to 1/sec(θ) - sec(θ).

Step-by-step explanation:

The expression tan(-θ) × sec(-θ) × cot(0) is equivalent to 1/sec(θ) - sec(θ).

To find the equivalent expression, let's substitute the values of the trigonometric functions into the expression:

tan(-θ) = -tan(θ)

sec(-θ) = sec(θ)

cot(0) = 1/tan(0) = 1/0, which is undefined

Since cot(0) is undefined, the expression is only defined when cot(0) is excluded. Thus, the equivalent expression is 1/sec(θ) - sec(θ).