Simplify (1-sec(x))(1+cos(x))

Problem

(1−sec(x))*(1+cos(x))

Solution

1. Expand the expression using the FOIL method (First, Outer, Inner, Last).

1+cos(x)−sec(x)−sec(x)*cos(x)

2. Apply the reciprocal identity sec(x)=1/cos(x) to the last term.

1+cos(x)−sec(x)−1/cos(x)⋅cos(x)

3. Simplify the product of the reciprocal terms.

1+cos(x)−sec(x)−1

4. Combine like terms by subtracting the constants.

cos(x)−sec(x)

Final Answer

(1−sec(x))*(1+cos(x))=cos(x)−sec(x)

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