How do I transform $-2\tan x + \sec^2 x $ into the form $(a +b \tan x)^2$?

Question

How does $\frac{1}{\cos^2 x}$ translate into $\tan^2$? I felt like I missed a formula or so, but what?

It obviously asks to turn it into quadratic form of $\tan,$ but I’m lacking $\sin^2$ .

Answer 1

Hint: Use the following well-known identity

$$\sec^2 x = 1+\tan^2 x$$

which yields

$$-2\tan x+\tan^2 x+1$$

Answer 2

You may use the identity $$ \sec^2 x = 1 + \tan^2 x $$