Question

50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answer 1

C

Explanation:

cot²θ = 1/tan²θ

plug this in to get

1/(1/tan²θ + 1)

1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ

we then have

1/((1+tan²θ)/tan²θ)

1/(x/y) = y/x, so this is equal to

tan²θ/(1+tan²θ)

tan²θ = sin²θ/cos²θ, so plug this in to get

(sin²θ/cos²θ)/(1+sin²θ/cos²θ)

1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ

sin²θ + cos²θ = 1, so we have

(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get

(sin²θ/cos²θ)/(1/cos²θ)

(a/b)/(c/d) = (d/c) * (a/b), so we have

(sin²θ/cos²θ)/(1/cos²θ) = cos²θ/1 * sin²θ/cos²θ = sin²θ