prove this identity

[Guest]

I got frusterated with this question:

Prove this identity:
1-tan^2x/(1+ tan^2x) = cos^2x-sin^2x




help! show the steps too :wink:

Anna

 

[Matt]

Hi Anna,

For this problem you can start with the left-hand side and try to work your way to the right. Begin by multiplying both the numerator and denominator by cos²x:

Can you finish it from here (there's only one more step to go)?

 

[Guest]

I get how to do it after the last step you did, but I don't get what you did on the 2nd step. how come you multiplied by cos^2X? cuz if you do that, don't you have to do it to the other side too, which makes it not work..

 

[Guest]

how come you multiplied by cos^2X?

He didn't; he multiplied by cos^2(x) / cos^2(x), which is 1.