Given: The first derivative of $\tan x$ is $1/\cos^2 x$
So the derivative of $\tan x$ when $x=0$ should be $1$. This derivative times $x$ should be a term in the Taylor expansion (the term then being $x$).
However, in the answer it says that expansion is $1 - x^3/3\cdots$. Where did the $x$ go?