Question

Which of the following is equivalent to sin(−θ)cosθcsc(−θ)sec(−θ) for all values of θ for which sin(−θ)cosθcsc(−θ)sec(−θ) is defined?

a. tanθ
b. 1
c. −1
d. −tanθ

Answer 1

The expression sin(-θ)cosθcsc(-θ)sec(-θ) can be simplified to sinθ * cosθ * cscθ * secθ.

Step-by-step explanation:

The expression sin(-θ)cosθcsc(-θ)sec(-θ) can be simplified using trigonometric identities.

1. The identity sin(-θ) = -sinθ, cos(-θ) = cosθ, csc(-θ) = -cscθ, and sec(-θ) = secθ can be used.
2. By substituting these values, we get -sinθ * cosθ * (-cscθ) * secθ.
3. By rearranging the terms, we can simplify the expression to sinθ * cosθ * cscθ * secθ.

Therefore, the expression sin(-θ)cosθcsc(-θ)sec(-θ) is equivalent to sinθ * cosθ * cscθ * secθ.