Question

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

cos(−θ)⋅tan(−θ)⋅cscθ
Select the correct answer below:


−sinθ
1
sinθ
−1

Answer 1

We can use the trigonometric identities to simplify the expression:

cos(-θ) = cos(θ) (even function)

tan(-θ) = -tan(θ) (odd function)

csc(θ) = 1/sin(θ)

Substituting these values, we get:

cos(θ) * (-tan(θ)) * (1/sin(θ))

= -cos(θ) * (tan(θ)/sin(θ))

= -cos(θ) * (sin(θ)/cos(θ)) * (1/sin(θ))

= -1

Therefore, the expression is equivalent to -1.

Hence, the correct answer is (D) -1.