quick log question?

Question

why when you simplify 2-X / X^2 that it equals 2/X and not -2/X ?

while I'm at it, I have another log question...
how do you simplify
2(cos^2 2X + sin^2 2X) / cos^2 2X
Explanation would be good! Thanks.

Answer 1

Yeah, it looks like a typo. (2x)/(x^2) = 2/x.

(2-x)/(x^2) = 2/(x^2) - 1/x

Now for your other trig question ...

2[cos^2(2x) + sin^2(2x)] / cos^2(2x)

On top, you have a trig identity: cos^2() + sin^2() = 1

2[cos^2(2x) + sin^2(2x)] / cos^2(2x) = 2 / cos^2(2x)

But sec() = 1/cos(), so

2 / cos^2(2x) = 2 sec^2(2x)

Answer 2

2(cos^2 2X + sin^2 2X) / cos^2 2X =
2(cos^2 2X/cos^2 2X + sin^2 2X/cos^2 2X) =
2(1 + tan^2 2x

Answer 3

2(cos² 2X + sin² 2X) / cos² 2X

since cos² θ + sin² θ = 1,
= 2(1)/cos² 2X

therefore,
= 2/cos² 2X

since 1/cos θ = sec θ,
= 2 sec² 2X

^_^
^_^

Answer 4

looks like a typo

(2X) / (x^2) = 2/X

(2*X) / (x^2) = 2/X


(2-X) / (x^2) = (2/(X^2)) - (1/X)