Answer:
f(x) = cos(x)
Step-by-step explanation:
Given the expression
[tex]tan(x)csc(c) = \frac{1}{f(x)}[/tex]
Recall that;
[tex]tan(x) = \frac{sin(x)}{cos(x)} \\csc(x) = \frac{1}{sin(x)} \\[/tex]
Substitute into the given expression
[tex]tan(x)csc(c) = \frac{1}{f(x)}\\\frac{sin(x)}{cos(x)} \frac{1}{sin(x)} = \frac{1}{f(x)}\\\frac{1}{cos(x)} = \frac{1}{f(x)}[/tex]
Cross multiply
[tex]cos(x) = f(x)\\Swap\\f(x) = cos(x)[/tex]
