# X=a(cosθ+cos2θ),y=b(sinθ+sin2θ) Remove θ By applying Elimination Methods ??

Given

From (1) and (2) we get

Now by (1) we have

Combining (3) and (4) we get

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To eliminate θ from the given equations, we can use the trigonometric identity:

[ \sin^2 θ + \cos^2 θ = 1 ]

By rearranging the terms in the given equations, we can express sin2θ and cos2θ in terms of sinθ and cosθ:

[ \sin2θ = 2\sinθ\cosθ ] [ \cos2θ = \cos^2θ - \sin^2θ ]

Substitute these expressions into the equations for x and y:

[ x = a(\cosθ + \cos2θ) = a\cosθ + a(\cos^2θ - \sin^2θ) ] [ y = b(\sinθ + \sin2θ) = b\sinθ + b(2\sinθ\cosθ) ]

Now, we can express cos^2θ and sin^2θ using the trigonometric identity:

[ \cos^2θ = 1 - \sin^2θ ] [ \sin^2θ = 1 - \cos^2θ ]

Substitute these expressions into the equations for x and y:

[ x = a\cosθ + a(1 - \sin^2θ - (1 - \cos^2θ)) ] [ y = b\sinθ + b(2\sinθ\cosθ) ]

Now, we have the equations for x and y without θ.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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