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Find the equation of the tangent and the normal to the following curves at the indicated points: 

x = θ + sin θ, y = 1 + cos θ at θ = π/2.

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finding slope of the tangent by differentiating x and y with respect to theta

\(\frac{dx}{d\theta}=1+cos\theta\)

\(\frac{dy}{d\theta}=-sin\theta\)

Dividing both the above equations

\(\frac{dy}{dx}=-\frac{sin\theta}{1+cos\theta}\)

m(tangent) at theta ( \(\pi/2\) ) = – 1

normal is perpendicular to tangent so, m1m2 = – 1

m(normal) at theta ( \(\pi/2\) ) = 1

equation of tangent is given by y – y1 = m(tangent)(x – x1)

\(y-1=-1(x-\frac{\pi}{2}-1)\)

equation of normal is given by y – y1 = m(normal)(x – x1)

\(y-1=1(x-\frac{\pi}{2}-1)\)

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