In my Pre Calculus (with trig) class we're going over Trigonometric Identities. I honestly have no idea how to work this problem. Just as an example, one the the problems is:

1-tan^2x = (cos2x) / (cos^2 2x)

What I guess we're supposed to do is prove how the two sides equal each other, but I am not sure of how to do this, and with my final comming on this week (on Tuesday) I'm in a bit of a jam.

Any help would be greatly appreciated.
Thanks in advance,
Son of Dwight

Not only is your answer a day or two late. I'm better at chemistry than I am at trig.
I really had to struggle with it too.

For your equation instead of using the identities would it be possible to look at a few special cases..

If x= 0 radians.. then
1-tan^2(0)= 1 and Cos(2x)=cos(0)=1 Cos^2(0)=1
1/1= 1.... cool equation works..
Let x=60 degrees.... -2=-2... still ok

For an equation to be true it needs to be true all the time.. let x= 90 degrees or 1/2 pi radians..
Tangent x= large number
Tangent Squared of x = a bigger number..
1-big number = a large negative number..

Cos of 2*90 degrees or 1/2 Pi= -1
-1<> large negative number..
the equation does not hold up for all cases.

again the disclaimer.. that I'm not good at math
I was stumped 2x viewing your post and tried this method tonight to exclude the truth of an equation by absurdity with special cases of x.
be sure to check my work.