Simplify (1-sin(x))/(cos(x))

Problem

(1−sin(x))/cos(x)

Solution

1. Identify the expression as a fraction involving trigonometric functions that can be split into two separate terms.

2. Distribute the denominator cos(x) to both terms in the numerator.

1/cos(x)−sin(x)/cos(x)

3. Apply the reciprocal identity sec(x)=1/cos(x) and the quotient identity tan(x)=sin(x)/cos(x)

sec(x)−tan(x)

Final Answer

(1−sin(x))/cos(x)=sec(x)−tan(x)

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