Question

cosx (cos(-x) - tan(-x)) = cosx (cos(x) + tan(x) Why does cos(x) become positive?

Answer 1

Because cosine is an even function.

Answer 2

A function f(x) is even if f(-x) = f(x).

Answer 3

In the case of tangent, you have
\[+\tan (-x)\\
+\frac{\sin (-x)}{\cos (-x)}\\
+\frac{-\sin x}{\cos x}\;\;\;\;\;\;\;\;\text{(because sine is an odd function)}\\
-\frac{\sin x}{\cos x}\\
-\tan x\]
And for odd functions:
A function f(x) is odd if f(-x) = -f(x).

Answer 4

oh yes i forgot, thanks