Simplify tan(x)-sec(x)

Problem

tan(x)−sec(x)

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the fundamental identities tan(x)=sin(x)/cos(x) and sec(x)=1/cos(x)

tan(x)−sec(x)=sin(x)/cos(x)−1/cos(x)

2. Combine the fractions since they share a common denominator of cos(x)

sin(x)/cos(x)−1/cos(x)=(sin(x)−1)/cos(x)

Final Answer

tan(x)−sec(x)=(sin(x)−1)/cos(x)

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