Can 2cos^4x-1 be substituted for cos^4x?

Question

anonymous · Answer

No, what makes you think so?

anonymous · Answer

I was just wondering because 2cos^2-1=cos2x and when I did what I asked above, I got the right answer however I'm having doubts about it.

anonymous · Answer

would it be 4cos^4x?

anonymous · Answer

They are different, getting the correct answer was probably coincidence. :)

Did you mean for the second one to be cos(4x) instead of cos^4(x)?

anonymous · Answer

I'm confused now :s I'm just trying to solve a trig identity. cos^4x-sin^4x/1-tan^4x...could you help me with that?

anonymous · Answer

Just to make sure we are on the same page, is this the identity?

$$ \frac {\cos^4 x - \sin^4 x} {1 - \tan^4 x} $$

anonymous · Answer

yep

anonymous · Answer

To solve it you need to factorize the numerator. 

$$ \cos^4 x - \sin^4 x = (\cos^2 x - \sin^2 x)(\cos^2 x + \sin^2 x) $$
After that it is pretty easy, give it a shot and let me know if you get stuck.

anonymous · Answer

Oh wait it is even easier, you write the denominator as:

$$ 1 - \tan^4 x = 1 - \frac {\sin^4 x} {\cos^4 x} = \frac {\cos^4 x - \sin^4 x} {\cos^4 x} $$

anonymous · Answer

Okay now I see it. I was missing some identities before. Thank again for helping me. :)