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Normal to x = theta + sin theta, y = 1 + cos theta at theta = pi/2

The same question, asked 2 times: 2 May 2023 S2, 3 May 2023 S1. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S2

    139
    The equation of normal to the curve x=θ+sin⁡θ,  y=1+cos⁡θx=\theta+\sin\theta,\; y=1+\cos\theta at θ=π2\theta=\frac{\pi}{2} is

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  2. Question 2

    3 May 2023 S1

    135
    The equation of the normal to the curve x=θ+sin⁡θ, y=1+cos⁡θx=\theta+\sin\theta,\ y=1+\cos\theta at θ=π2\theta=\frac{\pi}{2} is

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