Simplify tan(theta)-sec(theta)

Problem

tan(θ)−sec(θ)

Solution

1. Express in terms of sine and cosine by using the fundamental trigonometric identities tan(θ)=sin(θ)/cos(θ) and sec(θ)=1/cos(θ)

tan(θ)−sec(θ)=sin(θ)/cos(θ)−1/cos(θ)

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

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

Final Answer

tan(θ)−sec(θ)=(sin(θ)−1)/cos(θ)

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