Simplify (tan(theta))/(sec(theta))

Problem

tan(θ)/sec(θ)

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the fundamental 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. Multiply the numerator by the reciprocal of the denominator to simplify the complex fraction.

sin(θ)/cos(θ)⋅cos(θ)/1

3. Cancel the common factor of cos(θ) from the numerator and the denominator.

sin(θ)

Final Answer

tan(θ)/sec(θ)=sin(θ)

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