 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2018/6/solution

(sec θ + tan θ) / (sec θ + tan θ)

\int sec θ d θ = \int \frac{s e c ^{2} θ + s e c θ t a n θ}{s e c θ + t a n θ} d θ = lo g ∣ sec θ + tan θ ∣ + C .

The numerator is the derivative of the denominator. The formula holds on any real interval avoiding zeros of

cos θ

; on such an interval

sec θ + tan θ

cannot vanish because

(sec θ + tan θ) (sec θ - tan θ) = 1

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