Simplify (cos(2x))/(cos(x))

Problem

cos(2*x)/cos(x)

Solution

1. Identify the double angle identity for cos(2*x) that involves cos(x)

2. Apply the formula cos(2*x)=2*cos2(x)−1 to the numerator.

(2*cos2(x)−1)/cos(x)

3. Distribute the division by cos(x) to each term in the numerator.

(2*cos2(x))/cos(x)−1/cos(x)

4. Simplify the first term by canceling cos(x) and rewrite the second term using the secant identity sec(x)=1/cos(x)

2*cos(x)−sec(x)

Final Answer

cos(2*x)/cos(x)=2*cos(x)−sec(x)

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