The equation of the tangent to the curve x = t cost, y=t sin ⁡t at the origin, is

The equation of the tangent to the curve  at the origin, is

1. A

$x=0$

2. B

$y=0$

3. C

4. D

$x-y=0$

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Solution:

We have,

At the origin, we have

The slope of the tangent at  is

$\frac{dy}{dx}={\left(\frac{dy}{\frac{dt}{dx}}\right)}_{t=0}={\left(\frac{\mathrm{sin}t+t\mathrm{cos}t}{\mathrm{cos}t-t\mathrm{sin}t}\right)}_{t=0}=0.$

So, the equation of the tangent at the origin is

.

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