Simplify (cos(x))/(sec(x))

Problem

cos(x)/sec(x)

Solution

1. Identify the trigonometric identity for the secant function.

sec(x)=1/cos(x)

2. Substitute the identity into the denominator of the original expression.

cos(x)/1/cos(x)

3. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

cos(x)⋅cos(x)

4. Multiply the terms to reach the final simplified form.

cos2(x)

Final Answer

cos(x)/sec(x)=cos2(x)

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