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)

2. A)

Step-by-step explanation:

$1) \\\\\theta = \frac{\pi}{3} \\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2} \\\\csc \frac{\pi}{3} = \frac{2}{\sqrt{3}} = \frac{2 \sqrt{3}}{\sqrt{3}\sqrt{3}} \\\\sin\theta * csc\theta = \frac{\sqrt{3}}{2} * \frac{2}{\sqrt{3}} = \frac{2 * \sqrt{3}}{2 * \sqrt{3}} = 1 \\\\\\2) \\\\\theta = \frac{\pi}{4} \\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2} \\\\sec \frac{\pi}{4} = \frac{2}{\sqrt{2}} = \sqrt{2} \\\\cos\theta * sec\theta = \frac{\sqrt{2}}{2} * \frac{2}{\sqrt{2}} = \frac{2 * \sqrt{2}}{2 * \sqrt{2}} = 1$