Simplify sec(x)-tan(x)

Problem

sec(x)−tan(x)

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the reciprocal and quotient identities.

sec(x)=1/cos(x)

tan(x)=sin(x)/cos(x)

2. Substitute these expressions back into the original subtraction.

1/cos(x)−sin(x)/cos(x)

3. Combine the fractions since they share a common denominator.

(1−sin(x))/cos(x)

Final Answer

sec(x)−tan(x)=(1−sin(x))/cos(x)

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