Write the following in terms of sin(θ) and cos(θ); then simplify if possible.
sec(θ) / tan(θ) =
To write sec(θ) / tan(θ) in terms of sin(θ) and cos(θ), we need to recall the definitions of secant and tangent:
sec(θ) = 1 / cos(θ)
tan(θ) = sin(θ) / cos(θ)
Substituting these into the expression, we have:
sec(θ) / tan(θ) = (1 / cos(θ)) / (sin(θ) / cos(θ))
To simplify this expression, we can multiply the numerator and denominator by the reciprocal of the denominator:
sec(θ) / tan(θ) = (1 / cos(θ)) * (cos(θ) / sin(θ))
= 1 * (cos(θ) / cos(θ)) / sin(θ)
= cos(θ) / sin(θ)
Therefore, sec(θ) / tan(θ) = cos(θ) / sin(θ).