(a)

The curve is .

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Differentiate on each side with respect to .

Slope of the tangent is derivative of the function.

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The curve has horizontal tangent, when slope of the horizontal tangent is zero.

Cosine double angle formula: .

and .

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If , then .

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If , then .

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x- coordinates of the curve, where it has horizontal tangent are . 

x- coordinates of the curve, where it has horizontal tangent are .