To simplify the expression tan(x) * sec(x), we should first recall the definitions of the tangent and secant functions in terms of sine and cosine. The tangent function can be expressed as:
tan(x) = sin(x) / cos(x)
And the secant function is defined as:
sec(x) = 1 / cos(x)
Substituting these definitions into the original expression gives:
tan(x) * sec(x) = (sin(x) / cos(x)) * (1 / cos(x))
This means that an acceptable first step in simplifying the expression tan(x) * sec(x) would be to substitute these definitions. Doing so allows us to combine and manipulate the terms more easily, leading to a clearer and simpler form:
sin(x) / cos^2(x)
Thus, a solid first step is to rewrite the functions in terms of sine and cosine, as it sets a strong foundation for further simplification.