proving an identity

[xc630]

Hi I need some help proving this identity

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

I tried replacing (1+tan^2x) with sec^2x and cross multiplied but I didn't get very far. I would appreciate any help. Thanks.

 

[Unco]

I tried replacing (1+tan^2x) with sec^2x

Good. Finish it: tan^2(x) = ?

 

[xc630]

Tan^2(x) = sec^2(x) -1 but I don't undersatand where you are going with it

 

[Unco]

I was thinking of two possible answers. You have chosen one of them. Go with it. 1 - tan^2(x) = 1 - ( . . .

 

[xc630]

Ok so I have:

1-tan^2(x)= cos 2x (sec^2x)

Then

1-tan^2(x) = 2cos^2(x)-1 (sec^2x)

Where should I go from here?

 

[Unco]

We do not know that equality holds, so deal with one side at a time.

LHS = [1 - (sec^2(x) - 1)]/(sec^2(x))

Show this equals the RHS.

 

[tsh44]

O thanks I got 2cos^2(x)-1 which equals 2cosx