# Let $x = \theta + \cos\theta, \; y = \theta - \sin\theta$ represents parametric form of a curve, then slope of tangent at a general point is ? Option 1) $\frac{1 - \cos\theta}{1 - \sin\theta}$ Option 2) $\frac{1 + \cos\theta}{1 - \sin\theta}$ Option 3) $\frac{1 - \cos\theta}{1 + \sin\theta}$ Option 4) $\frac{1 + \cos\theta}{1 + \sin\theta}$

As we have learned

Slope of tangent for parametric form -

$M_{T}=\frac{dy}{dt}.\frac{dt}{dx}$

$=\frac{f'_{y}}{f'_{x}}$

$and\:find \:M_{T}\:at\:(t)$

- wherein

$Where\:\:y=f(t)\:\:\:and\:\:\:x=f(t)$

Slope of tangent = $\frac{dy}{dx} =\frac{\frac{dy}{d\theta }}{\frac{dx}{d\theta }}= \frac{1- \cos \theta }{1- \sin \theta }$

Option 1)

$\frac{1 - \cos\theta}{1 - \sin\theta}$

Option 2)

$\frac{1 + \cos\theta}{1 - \sin\theta}$

Option 3)

$\frac{1 - \cos\theta}{1 + \sin\theta}$

Option 4)

$\frac{1 + \cos\theta}{1 + \sin\theta}$

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