Problem 31E

31. (a) Use the Quotient Rule to differentiate the function

$$ f(x)=\frac{\tan x-1}{\sec x} $$

(b) Simplify the expression for $f(x)$ by writing it in terms of $\sin x$ and $\cos x$, and then find $f^{\prime}(x)$.

(c) Show that your answers to parts (a) and (b) are equivalent.

 

Step-by-Step Solution