If sec(θ)=cosec(42°), what is the value of θ?
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Correct answer: A
Explanation
Given:
sec(θ) = cosec(42°)
By the formula:
secθ = 1 / cosθ
cosecA = 1 / sinA
secθ = cosec42°
1 / cosθ = 1 / sin42°
cosθ = sin42°
sin42° = cos(90° − 42°)
= cos48°
Therefore,
cosθ = cos48°
θ = 48°