## anonymous 4 years ago tan^2 x = 1-cos2x/ 1+ cos2x true or false?

1. anonymous

That would be true. It' an identity.

2. anonymous

It's not an identity. Does tan^2x = 1-(cos2x/1)? I'm certain it doesn't. It does, however, equal to (1-cos2x)/2. This is an example of a half-angle identity.

3. anonymous

er....er

4. anonymous

$\frac{ 1-\cos 2x }{ 1+\cos 2x }=\frac{ 1-(1-2\sin^2x) }{ 1+(2\cos^2x-1) }=\frac{ 2\sin^2x }{2\cos^2x }=\tan^2x$

5. anonymous

so its true.

6. anonymous

um 0.0 :/

7. anonymous

something wrong?

8. anonymous

you guys are confusting me 0.o true or no?

9. anonymous

the first i did was to use the double angle formula for sine and cosine. then it was simplified, then since the ratio of sine and cosine is tangent, then the next step is obvious.