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Acute angle between the lines of a pair, then the value of a trigonometric expression in it

The same question, asked 2 times: 15 Apr 2026 S1*, 16 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    15 Apr 2026 S1

    57
    If θ\theta is the acute angle between the lines represented by the equation x2−3xy+2y2=0x^2 - 3xy + 2y^2 = 0, then 3sin⁡θ+2cos⁡θ3sin⁡θ−2cos⁡θ=\dfrac{3\sin\theta + 2\cos\theta}{3\sin\theta - 2\cos\theta} =

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  2. Question 2

    16 Apr 2026 S2

    56
    If θ\theta is the acute angle between the lines 2x2+7xy+3y2=02x^2 + 7xy + 3y^2 = 0, then the value of 2cos⁡θ−3sin⁡θ4sin⁡θ+5cos⁡θ=…\dfrac{2\cos\theta - 3\sin\theta}{4\sin\theta + 5\cos\theta} = \ldots

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