To simplify the expression tan(x) sec(x), it’s important to recall the definitions of these two trigonometric functions. The tangent and secant functions can be expressed in terms of sine and cosine:
- tan(x) = sin(x) / cos(x)
- sec(x) = 1 / cos(x)
Using these definitions, we can rewrite the expression:
tan(x) sec(x) = (sin(x) / cos(x)) * (1 / cos(x))Now, combining the fractions:
tan(x) sec(x) = sin(x) / cos^2(x)This step effectively simplifies the initial expression into a single fraction, making it easier to work with for further calculations or integrations, if needed. Thus, the first step we took—rewriting the trigonometric functions in terms of sine and cosine—was crucial in simplifying the expression.