Question

ABC is a triangle inscribed in a circle with centre O. Let α = ∠ BAC, where 45° < α < 90° Let β = ∠BOC. Which one of the following is correct?

a. cosβ = (1 - tan²α)/(1 + tan²α)

b. cosβ = (1 + tan²α)/(1 - tan²α)

c. cosβ = 2tanα/(1 + tan²α)

d. sinβ = 2sin²α

Answer 1

Correct option  a. cosβ = (1 - tan²α)/(1 + tan²α)

Explanation:

cosβ = cos2α = (1 - tan²α)/(1 + tan²α)