If \frac{ \sin ⁡\theta −\cos ⁡\theta + 1}{ \sin ⁡\theta + \cos ⁡\theta −1} = p sec θ + q tan θ, where 0 < θ < \frac{\pi }{2}, then what is p + q equal to?

UPSC CDS I 2024 Math Paper

Question : 52 of 100

Marks: +1, -0

If ‌

sin‌⁡θ‌−cos‌⁡θ‌‌+‌1

sin‌⁡θ‌‌+‌cos‌⁡θ‌−1

= p sec θ + q tan θ, where 0 < θ < ‌

π‌

, then what is p + q equal to?

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