Question

Show that the functions f and g are identically equal.

$f\left(x\right)=\sin x·\tan x,g\left(x\right)=secx-\cos x$

Short answer

Yes, the functions are identically equal.

Step-by-step solution

Step 1. Given Information

The given functions are$f\left(x\right)=\sin x·\tan x,g\left(x\right)=secx-\cos x$

Step 2. Calculation

Simplify any one function and determine whether they are equal or not to the other function.

$$\begin{gathered} g\left(x\right)=secx-\cos x \\ =\frac{1}{\cos x}-\cos x \\ =\frac{1-{\cos }^{2}x}{\cos x} \\ =\frac{{\sin }^{2}x}{\cos x} \\ =\sin x\tan x \\ =f\left(x\right) \end{gathered}$$

Thus, both the functions are equal.