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Consider the function fn(θ) = tan(θ/2)(1 + sec²θ)(1 + sec⁴θ)... (1 + sec²ⁿθ). Which of the following is true?
- f₂(π/16) equals 1
- f₃(π/32) equals 1
- f₄(π/64) equals 1
- f₅(π/128) equals 1
Correct answer: f₄(π/64) equals 1
Solution
The correct statement is f₄(π/64) equals 1, which can be determined by analyzing the function fn(θ) and evaluating it for the given values.
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