Question

Does anyone know how to solve these two similar problems? I am very confused. Please provide a good description of how to solve this question.

1. Given that θ= π/3 , which of the following shows that sinθcscθ = 1?
A. (√2/2)(√2) = 1
B. (√3/2)(2√3/3) = 1
C. (1/2)(2) = 1

2. Given that θ = π/4, which of the following shows that cosθsecθ = 1?
A. (√2/2)(√2) = 1
B. (√3/2)(2√3/3) = 1
C. (1/2)(2) = 1

Answer 1

Answer: 1 B and 2 A

:)))))

Answer 2

1. B)

2. A)

Explanation:

`1) \\\\\theta = (\pi)/(3) \\sin (\pi)/(3) = (√(3))/(2) \\\\csc (\pi)/(3) = (2)/(√(3)) = (2 √(3))/(√(3)√(3)) \\\\sin\theta * csc\theta = (√(3))/(2) * (2)/(√(3)) = (2 * √(3))/(2 * √(3)) = 1 \\\\\\2) \\\\\theta = (\pi)/(4) \\cos (\pi)/(4) = (√(2))/(2) \\\\sec (\pi)/(4) = (2)/(√(2)) = √(2) \\\\cos\theta * sec\theta = (√(2))/(2) * (2)/(√(2)) = (2 * √(2))/(2 * √(2)) = 1`