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For unit vectors a and b at angle theta: |a + b| / |a - b| in terms of theta

The same question, asked 2 times: 20 Apr 2025 S2*, 15 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    112
    If aˉ\bar{a} and bˉ\bar{b} are unit vectors and θ\theta is the angle between them, then tan⁡θ2=\tan\frac{\theta}{2}=

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  2. Question 2

    15 Apr 2026 S1

    88
    If aˉ\bar{a} and bˉ\bar{b} are unit vectors and θ (0<θ<π)\theta\ (0 < \theta < \pi) is the angle between them, then the value of ∣aˉ+bˉ∣∣aˉ−bˉ∣\dfrac{|\bar{a} + \bar{b}|}{|\bar{a} - \bar{b}|} is equal to...

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