- #1
danago
Gold Member
- 1,123
- 4
If [tex]z=cis\theta[/tex], verify that [tex]
\tan \theta = \frac{{z - z^{ - 1} }}{{i(z + z^{ - 1} )}}
[/tex]. Use this result to prove that [tex]
\cos (2\theta ) = \frac{{1 - \tan ^2 \theta }}{{1 + \tan ^2 \theta }}
[/tex]
Ok, I've managed to verify the first equation given, but I am not really sure how to use it to prove the second identity. I am really not sure where to start. If somebody could give me a hint about where to start id be very appreciative.
Thanks,
Dan.
\tan \theta = \frac{{z - z^{ - 1} }}{{i(z + z^{ - 1} )}}
[/tex]. Use this result to prove that [tex]
\cos (2\theta ) = \frac{{1 - \tan ^2 \theta }}{{1 + \tan ^2 \theta }}
[/tex]
Ok, I've managed to verify the first equation given, but I am not really sure how to use it to prove the second identity. I am really not sure where to start. If somebody could give me a hint about where to start id be very appreciative.
Thanks,
Dan.