Help with proving whether or not the equation is a trig identity? Medal and fan.

I need help proving whether or not cos^2x(1+tan2x)=1 is an identity

Thanks(:

Question

Help with proving whether or not the equation is a trig identity? Medal and fan.

I need help proving whether or not cos^2x(1+tan2x)=1 is an identity

Thanks(:

loser66 · Answer

yes, it is
open the bracket, what do you have?

anonymous · Answer

1-cos(2x)/2 *(1 + 1-cos(2x)/1+cos(2x)

loser66 · Answer

$$cos^2(x)(1+tan^2(x))= cos^2(x) + cos^2(x) tan^2(x)$$
now replace $tan ^2 (x) = \dfrac{sin^2(x)}{cos^2(x)}$ what do you have?

anonymous · Answer

1-cos(2x)/ 1+ cos(2x) right?

loser66 · Answer

nope. 
$$cos^2(x)(1+tan^2(x))= cos^2(x) + cos^2(x) tan^2(x)=cos^2(x) +cos^2(x)\dfrac{sin^2(x)}{cos^2(x)}\= cos^2(x)+sin^2(x)=1$$
that is identity

anonymous · Answer

Oh, I was going to far. I was giving the identities of the sin^2(x) and cos^2(x) sorry. Thanks, I understand that(: