$\"\"$

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The function is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Sum rule of derivatives : $\"\"$ .

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$\"\"$

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Constant multiple and the power rule: $\"\"$ .

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Derivative of a sine function : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Slope of the horizontal tangent line is $\"\"$ .

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To find the points at which the function has a horizontal tangent line, equate $\"\"$ .

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$\"\"$

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$\"\"$

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Cosine function ranges between $\"\"$ and $\"\"$ .

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So the solution of $\"\"$ does not exits.

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Hence $\"\"$ does not have horizontal tangent line.

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$\"\"$

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$\"\"$ does not have horizontal tangent line.